Updates

AR0

Ihs Patent Count

0.01

us_all

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 14:06:43 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1071       
                Sample: 1 to 1071       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error  t-stat   p-value          
                lgdp                          0.4083008  1.0988219  0.3716 0.7102874          
                lpop                          0.1228244  0.4683003  0.2623 0.7931644          
                lgdp_sq                      -0.0025070  0.0469877 -0.0534 0.9574611          
                avg_temp                      0.0068327  0.0138781  0.4923 0.6225921          
                idAlaska                      0.1539210  0.9159737  0.1680 0.8665867          
                idArizona                     1.8382916  0.1616847 11.3696 < 2.2e-16 ***      
                idArkansas                   -0.7168372  0.2424386 -2.9568 0.0031851 **       
                idCalifornia                  3.2209333  0.8451921  3.8109 0.0001473 ***      
                idColorado                    2.2892983  0.2814646  8.1335 1.286e-15 ***      
                idConnecticut                 3.0186267  0.3035117  9.9457 < 2.2e-16 ***      
                idDelaware                    2.4677290  0.6843453  3.6060 0.0003271 ***      
                idDistrictofColumbia          0.7209092  0.9029629  0.7984 0.4248470          
                idFlorida                     1.6797514  0.5509056  3.0491 0.0023586 **       
                idGeorgia                     1.3623506  0.2966739  4.5921 4.974e-06 ***      
                idHawaii                     -0.5375363  0.6553705 -0.8202 0.4123051          
                idIdaho                       0.9916685  0.5205387  1.9051 0.0570690 .        
                idIllinois                    1.9602000  0.4422827  4.4320 1.042e-05 ***      
                idIndiana                     1.1123096  0.2309947  4.8153 1.708e-06 ***      
                idIowa                        0.5298050  0.2966688  1.7858 0.0744406 .        
                idKansas                      0.2676003  0.2590662  1.0329 0.3018922          
                idKentucky                    0.3155498  0.1558208  2.0251 0.0431362 *        
                idLouisiana                   0.1647656  0.1689486  0.9752 0.3296873          
                idMaine                       0.4117538  0.5864095  0.7022 0.4827496          
                idMaryland                    1.4447747  0.2005713  7.2033 1.190e-12 ***      
                idMassachusetts               2.9174353  0.3024931  9.6446 < 2.2e-16 ***      
                idMichigan                    2.3834103  0.4014407  5.9371 4.053e-09 ***      
                idMinnesota                   2.1991567  0.3389058  6.4890 1.384e-10 ***      
                idMississippi                 0.4722006  0.2609270  1.8097 0.0706553 .        
                idMissouri                    0.8799695  0.1879656  4.6815 3.258e-06 ***      
                idMontana                     0.3083292  0.6827426  0.4516 0.6516567          
                idNebraska                   -0.1643843  0.4368491 -0.3763 0.7067808          
                idNevada                      1.4762358  0.3362792  4.3899 1.260e-05 ***      
                idNewHampshire                1.8174434  0.5737393  3.1677 0.0015851 **       
                idNewJersey                   1.9694370  0.3208803  6.1376 1.225e-09 ***      
                idNewMexico                   1.7177252  0.3667735  4.6833 3.230e-06 ***      
                idNewYork                     2.6626958  0.6465340  4.1184 4.145e-05 ***      
                idNorthCarolina               1.9764854  0.2944006  6.7136 3.250e-11 ***      
                idNorthDakota                 0.0750847  0.8208691  0.0915 0.9271385          
                idOhio                        2.2808536  0.4021139  5.6722 1.867e-08 ***      
                idOklahoma                    0.7611425  0.1541392  4.9380 9.309e-07 ***      
                idOregon                      2.5699610  0.3076473  8.3536 2.308e-16 ***      
                idPennsylvania                2.2792968  0.4482964  5.0844 4.437e-07 ***      
                idRhodeIsland                 1.9239293  0.6117648  3.1449 0.0017128 **       
                idSouthCarolina               1.4289628  0.1549909  9.2197 < 2.2e-16 ***      
                idSouthDakota                -0.1192652  0.7452814 -0.1600 0.8728935          
                idTennessee                   0.3713279  0.2262445  1.6413 0.1010704          
                idTexas                       1.9897210  0.6710861  2.9649 0.0031027 **       
                idUtah                        1.2440041  0.3112346  3.9970 6.908e-05 ***      
                idVermont                     1.0331895  0.8500050  1.2155 0.2244714          
                idVirginia                    1.6074055  0.2678702  6.0007 2.785e-09 ***      
                idWashington                  2.0257263  0.3097028  6.5409 9.944e-11 ***      
                idWestVirginia                0.0530469  0.4050056  0.1310 0.8958200          
                idWisconsin                   1.9586318  0.3080220  6.3587 3.145e-10 ***      
                idWyoming                     1.3722310  0.9389396  1.4615 0.1442151          
                time2000                     -5.0285864  7.6219351 -0.6598 0.5095718          
                time2001                     -4.9954705  7.6254015 -0.6551 0.5125549          
                time2002                     -4.8482729  7.6269593 -0.6357 0.5251398          
                time2003                     -4.7417790  7.6255011 -0.6218 0.5342006          
                time2004                     -4.7608741  7.6272121 -0.6242 0.5326477          
                time2005                     -4.5013649  7.6296969 -0.5900 0.5553437          
                time2006                     -4.3788968  7.6336994 -0.5736 0.5663550          
                time2007                     -4.1804410  7.6326410 -0.5477 0.5840217          
                time2008                     -4.1300235  7.6306223 -0.5412 0.5884658          
                time2009                     -3.8883662  7.6334463 -0.5094 0.6105995          
                time2010                     -3.9579112  7.6369185 -0.5183 0.6043965          
                time2011                     -3.9668617  7.6381702 -0.5193 0.6036388          
                time2012                     -4.0186183  7.6430250 -0.5258 0.5991566          
                time2013                     -4.0807389  7.6362487 -0.5344 0.5931955          
                time2014                     -4.3547357  7.6353652 -0.5703 0.5685826          
                time2015                     -4.3362478  7.6404379 -0.5675 0.5704810          
                time2016                     -4.4248847  7.6428718 -0.5790 0.5627553          
                time2017                     -4.4929644  7.6414055 -0.5880 0.5566870          
                time2018                     -4.4565210  7.6386649 -0.5834 0.5597506          
                time2019                     -4.6152741  7.6369112 -0.6043 0.5457623          
                time2020                     -5.5564505  7.6437372 -0.7269 0.4674475          
                iis65                         1.9123133  0.3908942  4.8922 1.170e-06 ***      
                iis76                         1.1768405  0.3849653  3.0570 0.0022977 **       
                iis168                       -1.2116125  0.3984430 -3.0409 0.0024232 **       
                iis173                       -1.2857973  0.3940167 -3.2633 0.0011402 **       
                iis247                       -1.4694958  0.3883394 -3.7841 0.0001639 ***      
                iis249                       -1.3236139  0.3885699 -3.4064 0.0006857 ***      
                iis250                       -1.6153426  0.3886732 -4.1560 3.528e-05 ***      
                iis364                       -1.4553471  0.3777448 -3.8527 0.0001246 ***      
                iis525                        1.5290323  0.3807494  4.0158 6.387e-05 ***      
                iis527                       -1.3793819  0.3781501 -3.6477 0.0002789 ***      
                iis576                       -1.0505561  0.3851600 -2.7276 0.0064968 **       
                iis721                        1.1903262  0.3830399  3.1076 0.0019419 **       
                iis866                        1.7434342  0.3939148  4.4259 1.071e-05 ***      
                fesisAlaska.2007             -1.2192158  0.2010459 -6.0644 1.905e-09 ***      
                fesisAlaska.2014              0.7904637  0.2040454  3.8740 0.0001144 ***      
                fesisArkansas.2009            0.6482180  0.1723901  3.7602 0.0001801 ***      
                fesisConnecticut.2009        -0.5982914  0.1656534 -3.6117 0.0003200 ***      
                fesisDelaware.2014           -0.8178532  0.1849953 -4.4209 1.095e-05 ***      
                fesisDistrictofColumbia.2008 -1.2154298  0.2553178 -4.7605 2.230e-06 ***      
                fesisDistrictofColumbia.2011  1.4669191  0.2464042  5.9533 3.685e-09 ***      
                fesisHawaii.2001              1.3728067  0.3909467  3.5115 0.0004664 ***      
                fesisHawaii.2009             -0.4830059  0.1802577 -2.6795 0.0074991 **       
                fesisLouisiana.2011          -0.8326289  0.2163531 -3.8485 0.0001267 ***      
                fesisLouisiana.2015           1.0753087  0.2390419  4.4984 7.687e-06 ***      
                fesisMaine.2008               0.6999229  0.1688994  4.1440 3.715e-05 ***      
                fesisMississippi.2004        -1.3986445  0.2076588 -6.7353 2.819e-11 ***      
                fesisNebraska.2012            0.7383887  0.1675422  4.4072 1.166e-05 ***      
                fesisNevada.2012             -0.7433067  0.1854884 -4.0073 6.619e-05 ***      
                fesisNevada.2019              1.0401965  0.2964697  3.5086 0.0004714 ***      
                fesisOregon.2004             -0.7595870  0.2055449 -3.6955 0.0002319 ***      
                fesisRhodeIsland.2005        -0.8176507  0.1931060 -4.2342 2.515e-05 ***      
                fesisSouthCarolina.2008       0.8138095  0.1688143  4.8207 1.663e-06 ***      
                fesisSouthDakota.2008         1.2229023  0.1839370  6.6485 4.969e-11 ***      
                fesisSouthDakota.2019        -1.2583965  0.2845261 -4.4228 1.086e-05 ***      
                fesisTennessee.2005           0.6105224  0.1895153  3.2215 0.0013183 **       
                fesisWestVirginia.2013       -0.5877609  0.1692226 -3.4733 0.0005371 ***      
                fesisWyoming.2003            -0.8272521  0.2389653 -3.4618 0.0005603 ***      
                fesisWyoming.2017            -0.9102405  0.2377471 -3.8286 0.0001372 ***      
                fesisWyoming.2020             1.9366798  0.4256536  4.5499 6.057e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df p-value        
                Ljung-Box AR(1)   3.1879  1 0.07419 .      
                Ljung-Box ARCH(1) 3.5869  1 0.05824 .      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                 
                SE of regression    0.36470      
                R-squared           0.94193      
                Log-lik.(n=1071) -382.39447      
us_q25

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 14:06:18 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 903       
                Sample: 1 to 903       
                      
                SPECIFIC mean equation:      
                      
                                                  coef std.error  t-stat   p-value          
                lgdp                          0.519404  1.446762  0.3590 0.7196818          
                lpop                          0.400976  0.439162  0.9130 0.3614936          
                lgdp_sq                      -0.012287  0.054577 -0.2251 0.8219414          
                avg_temp                      0.022908  0.013607  1.6835 0.0926630 .        
                idArizona                     1.612787  0.151260 10.6623 < 2.2e-16 ***      
                idCalifornia                  2.853048  0.752354  3.7922 0.0001606 ***      
                idColorado                    2.371252  0.279825  8.4741 < 2.2e-16 ***      
                idConnecticut                 3.131560  0.296952 10.5457 < 2.2e-16 ***      
                idDelaware                    2.700855  0.618966  4.3635 1.448e-05 ***      
                idDistrictofColumbia          1.124298  0.818530  1.3736 0.1699655          
                idFlorida                     1.144018  0.496570  2.3038 0.0214880 *        
                idGeorgia                     1.046791  0.276275  3.7889 0.0001627 ***      
                idHawaii                     -0.774844  0.596417 -1.2992 0.1942630          
                idIdaho                       1.255046  0.503130  2.4945 0.0128158 *        
                idIllinois                    1.815963  0.412013  4.4075 1.189e-05 ***      
                idIndiana                     1.037456  0.224061  4.6302 4.264e-06 ***      
                idIowa                        0.639804  0.278810  2.2948 0.0220057 *        
                idKansas                      0.218737  0.236564  0.9246 0.3554302          
                idKentucky                    0.216175  0.145901  1.4817 0.1388273          
                idLouisiana                  -0.074335  0.163674 -0.4542 0.6498319          
                idMaine                       1.363863  0.562676  2.4239 0.0155769 *        
                idMaryland                    1.359471  0.202857  6.7016 3.897e-11 ***      
                idMassachusetts               2.941440  0.304465  9.6610 < 2.2e-16 ***      
                idMichigan                    2.353959  0.379744  6.1988 9.121e-10 ***      
                idMinnesota                   2.346710  0.335826  6.9879 5.897e-12 ***      
                idMissouri                    0.764652  0.181517  4.2126 2.813e-05 ***      
                idNevada                      1.592428  0.308826  5.1564 3.178e-07 ***      
                idNewHampshire                2.137318  0.532927  4.0105 6.628e-05 ***      
                idNewJersey                   1.864501  0.310972  5.9957 3.069e-09 ***      
                idNewMexico                   1.776135  0.341840  5.1958 2.591e-07 ***      
                idNewYork                     2.598424  0.593315  4.3795 1.348e-05 ***      
                idNorthCarolina               1.733335  0.274154  6.3225 4.283e-10 ***      
                idOhio                        2.140791  0.374442  5.7173 1.530e-08 ***      
                idOklahoma                    0.632230  0.139833  4.5213 7.079e-06 ***      
                idOregon                      2.648868  0.285227  9.2869 < 2.2e-16 ***      
                idPennsylvania                2.169198  0.417402  5.1969 2.576e-07 ***      
                idRhodeIsland                 2.174466  0.573496  3.7916 0.0001610 ***      
                idSouthCarolina               1.229780  0.136629  9.0009 < 2.2e-16 ***      
                idSouthDakota                 0.253364  0.714266  0.3547 0.7228935          
                idTennessee                   0.770142  0.168989  4.5574 5.992e-06 ***      
                idTexas                       1.546715  0.601231  2.5726 0.0102742 *        
                idUtah                        1.482256  0.299440  4.9501 9.055e-07 ***      
                idVermont                     1.488915  0.821431  1.8126 0.0702718 .        
                idVirginia                    1.464877  0.259837  5.6377 2.393e-08 ***      
                idWashington                  2.060039  0.307461  6.7002 3.935e-11 ***      
                idWisconsin                   2.042822  0.302100  6.7621 2.630e-11 ***      
                time2000                     -8.059962  9.585479 -0.8409 0.4006834          
                time2001                     -8.101472  9.587964 -0.8450 0.3983852          
                time2002                     -7.887850  9.591876 -0.8223 0.4111254          
                time2003                     -7.818781  9.594162 -0.8150 0.4153433          
                time2004                     -7.785658  9.599868 -0.8110 0.4175979          
                time2005                     -7.553239  9.604774 -0.7864 0.4318642          
                time2006                     -7.468415  9.609411 -0.7772 0.4372726          
                time2007                     -7.263460  9.609814 -0.7558 0.4499698          
                time2008                     -7.143503  9.606474 -0.7436 0.4573295          
                time2009                     -6.977285  9.604657 -0.7264 0.4677774          
                time2010                     -6.983727  9.609290 -0.7268 0.4675813          
                time2011                     -7.020416  9.611249 -0.7304 0.4653375          
                time2012                     -7.084575  9.615588 -0.7368 0.4614728          
                time2013                     -7.112107  9.610631 -0.7400 0.4595028          
                time2014                     -7.392397  9.612444 -0.7690 0.4420947          
                time2015                     -7.370782  9.618219 -0.7663 0.4437037          
                time2016                     -7.502710  9.620235 -0.7799 0.4356880          
                time2017                     -7.485611  9.620683 -0.7781 0.4367558          
                time2018                     -7.480671  9.621310 -0.7775 0.4370883          
                time2019                     -7.629548  9.622520 -0.7929 0.4280810          
                time2020                     -8.757563  9.622999 -0.9101 0.3630629          
                iis3                         -1.201887  0.323648 -3.7136 0.0002186 ***      
                iis5                         -1.116494  0.324002 -3.4459 0.0005988 ***      
                iis11                        -1.141991  0.323995 -3.5247 0.0004481 ***      
                iis18                        -1.433446  0.323738 -4.4278 1.085e-05 ***      
                iis126                       -1.072883  0.340157 -3.1541 0.0016704 **       
                iis131                       -1.322497  0.336533 -3.9298 9.241e-05 ***      
                iis135                       -1.145851  0.363139 -3.1554 0.0016630 **       
                iis205                       -2.625401  0.445108 -5.8983 5.423e-09 ***      
                iis207                       -1.497037  0.386635 -3.8720 0.0001168 ***      
                iis208                       -1.765082  0.386009 -4.5726 5.582e-06 ***      
                iis315                        1.221861  0.323472  3.7773 0.0001703 ***      
                iis322                       -1.416833  0.322308 -4.3959 1.253e-05 ***      
                iis358                       -1.282406  0.324356 -3.9537 8.379e-05 ***      
                iis362                       -1.442747  0.324342 -4.4482 9.888e-06 ***      
                iis368                       -1.203947  0.325403 -3.6999 0.0002305 ***      
                iis464                       -1.331498  0.322733 -4.1257 4.085e-05 ***      
                iis740                        1.708797  0.336404  5.0796 4.714e-07 ***      
                iis745                        1.188801  0.330978  3.5918 0.0003486 ***      
                iis746                        0.952035  0.330850  2.8775 0.0041150 **       
                iis755                       -1.458560  0.333178 -4.3777 1.359e-05 ***      
                iis757                       -1.122336  0.322840 -3.4764 0.0005356 ***      
                iis760                       -1.184935  0.322763 -3.6712 0.0002575 ***      
                fesisConnecticut.2009        -0.620966  0.141773 -4.3800 1.345e-05 ***      
                fesisDelaware.2014           -0.874802  0.159163 -5.4963 5.224e-08 ***      
                fesisDistrictofColumbia.2008 -0.717796  0.219243 -3.2740 0.0011062 **       
                fesisDistrictofColumbia.2012  0.975192  0.213516  4.5673 5.722e-06 ***      
                fesisHawaii.2001              1.647236  0.351729  4.6833 3.319e-06 ***      
                fesisHawaii.2005             -0.779303  0.188815 -4.1273 4.056e-05 ***      
                fesisHawaii.2015              1.151366  0.330633  3.4823 0.0005242 ***      
                fesisHawaii.2017             -1.012581  0.386831 -2.6176 0.0090222 **       
                fesisLouisiana.2011          -0.847914  0.184790 -4.5885 5.183e-06 ***      
                fesisLouisiana.2015           1.060583  0.204775  5.1793 2.824e-07 ***      
                fesisNevada.2012             -0.820551  0.160229 -5.1211 3.812e-07 ***      
                fesisNevada.2019              1.116717  0.253331  4.4081 1.185e-05 ***      
                fesisOregon.2004             -0.768589  0.176778 -4.3478 1.554e-05 ***      
                fesisRhodeIsland.2005        -0.826396  0.165246 -5.0010 7.018e-07 ***      
                fesisSouthCarolina.2008       0.771268  0.144222  5.3478 1.164e-07 ***      
                fesisSouthDakota.2008         0.980146  0.173837  5.6383 2.384e-08 ***      
                fesisUtah.2016               -0.563135  0.171412 -3.2853 0.0010634 **       
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df p-value        
                Ljung-Box AR(1)   0.1078  1 0.74266        
                Ljung-Box ARCH(1) 4.6031  1 0.03191 *      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                 
                SE of regression    0.31063      
                R-squared           0.94604      
                Log-lik.(n=903)  -172.56232      

Log Patent Count

0.01

us_all

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 13:55:48 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1071       
                Sample: 1 to 1071       
                      
                SPECIFIC mean equation:      
                      
                                                  coef std.error  t-stat   p-value          
                lgdp                         -0.817466  0.916508 -0.8919 0.3726508          
                lpop                          0.592368  0.388921  1.5231 0.1280624          
                lgdp_sq                       0.036635  0.039306  0.9321 0.3515444          
                avg_temp                      0.006058  0.011610  0.5218 0.6019276          
                idAlaska                      0.798679  0.763814  1.0456 0.2959879          
                idArizona                     1.524666  0.133936 11.3836 < 2.2e-16 ***      
                idArkansas                   -0.139757  0.219129 -0.6378 0.5237677          
                idCalifornia                  2.361599  0.694375  3.4010 0.0006990 ***      
                idColorado                    2.062720  0.234045  8.8133 < 2.2e-16 ***      
                idConnecticut                 2.878557  0.253175 11.3698 < 2.2e-16 ***      
                idDelaware                    2.631399  0.567312  4.6384 3.999e-06 ***      
                idDistrictofColumbia          1.355751  0.749103  1.8098 0.0706348 .        
                idFlorida                     1.063133  0.454870  2.3372 0.0196326 *        
                idGeorgia                     0.988608  0.244654  4.0408 5.752e-05 ***      
                idHawaii                      0.015172  0.543700  0.0279 0.9777433          
                idIdaho                       1.060506  0.433948  2.4439 0.0147106 *        
                idIllinois                    1.488725  0.362779  4.1037 4.412e-05 ***      
                idIndiana                     0.864819  0.190924  4.5297 6.652e-06 ***      
                idIowa                        0.596918  0.248050  2.4064 0.0162971 *        
                idKansas                      0.397059  0.215896  1.8391 0.0662066 .        
                idKentucky                    0.282119  0.130557  2.1609 0.0309514 *        
                idLouisiana                   0.181210  0.141777  1.2781 0.2015117          
                idMaine                       0.744443  0.485302  1.5340 0.1253646          
                idMaryland                    1.230881  0.165944  7.4175 2.625e-13 ***      
                idMassachusetts               2.635285  0.249577 10.5590 < 2.2e-16 ***      
                idMichigan                    1.926946  0.330468  5.8310 7.526e-09 ***      
                idMinnesota                   1.960427  0.281745  6.9581 6.381e-12 ***      
                idMississippi                 0.492238  0.217292  2.2653 0.0237150 *        
                idMissouri                    0.674890  0.155726  4.3338 1.620e-05 ***      
                idMontana                     0.643790  0.568110  1.1332 0.2574080          
                idNebraska                    0.201845  0.363835  0.5548 0.5791810          
                idNevada                      1.446246  0.280576  5.1546 3.087e-07 ***      
                idNewHampshire                1.872789  0.477645  3.9209 9.450e-05 ***      
                idNewJersey                   1.621387  0.263570  6.1516 1.125e-09 ***      
                idNewMexico                   1.651686  0.304680  5.4211 7.499e-08 ***      
                idNewYork                     2.053170  0.530112  3.8731 0.0001148 ***      
                idNorthCarolina               1.567299  0.242124  6.4731 1.530e-10 ***      
                idNorthDakota                 0.675553  0.682429  0.9899 0.3224605          
                idOhio                        1.802917  0.330048  5.4626 5.980e-08 ***      
                idOklahoma                    0.696108  0.128692  5.4091 8.000e-08 ***      
                idOregon                      2.297475  0.257666  8.9165 < 2.2e-16 ***      
                idPennsylvania                1.782709  0.367827  4.8466 1.464e-06 ***      
                idRhodeIsland                 1.956519  0.508566  3.8471 0.0001274 ***      
                idSouthCarolina               1.208152  0.129862  9.3033 < 2.2e-16 ***      
                idSouthDakota                 0.394956  0.619456  0.6376 0.5238962          
                idTennessee                   0.279847  0.187880  1.4895 0.1366842          
                idTexas                       1.291944  0.552366  2.3389 0.0195437 *        
                idUtah                        1.207885  0.260039  4.6450 3.874e-06 ***      
                idVermont                     1.305268  0.706274  1.8481 0.0648950 .        
                idVirginia                    1.296835  0.220248  5.8881 5.400e-09 ***      
                idWashington                  1.743429  0.255663  6.8192 1.618e-11 ***      
                idWestVirginia                0.115669  0.340103  0.3401 0.7338560          
                idWisconsin                   1.683460  0.256051  6.5747 7.996e-11 ***      
                idWyoming                     1.739556  0.780828  2.2278 0.0261229 *        
                time2000                     -0.133738  6.373409 -0.0210 0.9832630          
                time2001                     -0.096525  6.376299 -0.0151 0.9879251          
                time2002                      0.021755  6.377580  0.0034 0.9972790          
                time2003                      0.108516  6.376266  0.0170 0.9864252          
                time2004                      0.088659  6.377617  0.0139 0.9889114          
                time2005                      0.328622  6.379626  0.0515 0.9589289          
                time2006                      0.473152  6.382354  0.0741 0.9409189          
                time2007                      0.622041  6.381920  0.0975 0.9223741          
                time2008                      0.685663  6.380195  0.1075 0.9144407          
                time2009                      0.875599  6.382733  0.1372 0.8909153          
                time2010                      0.825243  6.385640  0.1292 0.8971994          
                time2011                      0.804861  6.386677  0.1260 0.8997410          
                time2012                      0.758061  6.390784  0.1186 0.9056029          
                time2013                      0.693877  6.384909  0.1087 0.9134834          
                time2014                      0.452983  6.384073  0.0710 0.9434483          
                time2015                      0.465581  6.388305  0.0729 0.9419167          
                time2016                      0.372971  6.390269  0.0584 0.9534697          
                time2017                      0.328957  6.389071  0.0515 0.9589478          
                time2018                      0.374926  6.386464  0.0587 0.9531983          
                time2019                      0.217162  6.385045  0.0340 0.9728754          
                time2020                     -0.624706  6.390995 -0.0977 0.9221530          
                iis65                         1.211273  0.338253  3.5810 0.0003595 ***      
                iis76                         0.923899  0.322577  2.8641 0.0042728 **       
                iis247                       -0.877696  0.333512 -2.6317 0.0086329 **       
                iis249                       -1.373239  0.356742 -3.8494 0.0001263 ***      
                iis250                       -1.644841  0.356706 -4.6112 4.545e-06 ***      
                iis364                       -1.125362  0.316476 -3.5559 0.0003951 ***      
                iis525                        1.352912  0.318951  4.2417 2.433e-05 ***      
                iis527                       -1.018840  0.316841 -3.2156 0.0013451 **       
                iis576                       -0.835056  0.322748 -2.5873 0.0098184 **       
                iis866                        1.360881  0.330010  4.1238 4.050e-05 ***      
                fesisAlaska.2007             -1.002223  0.168370 -5.9525 3.701e-09 ***      
                fesisAlaska.2014              0.691221  0.170848  4.0458 5.633e-05 ***      
                fesisArkansas.2006           -0.695042  0.225587 -3.0810 0.0021216 **       
                fesisArkansas.2009            0.898267  0.201519  4.4575 9.272e-06 ***      
                fesisConnecticut.2009        -0.546309  0.138615 -3.9412 8.696e-05 ***      
                fesisDelaware.2014           -0.887511  0.148038 -5.9951 2.876e-09 ***      
                fesisDistrictofColumbia.2008 -0.889044  0.209797 -4.2376 2.477e-05 ***      
                fesisDistrictofColumbia.2011  1.182208  0.206499  5.7250 1.383e-08 ***      
                fesisHawaii.2001              1.009582  0.327597  3.0818 0.0021164 **       
                fesisHawaii.2009             -0.607187  0.167336 -3.6286 0.0003001 ***      
                fesisHawaii.2016              0.633657  0.218852  2.8954 0.0038730 **       
                fesisLouisiana.2011          -0.694478  0.181268 -3.8312 0.0001358 ***      
                fesisLouisiana.2015           0.904990  0.200305  4.5180 7.019e-06 ***      
                fesisMaine.2011               0.539693  0.137387  3.9283 9.170e-05 ***      
                fesisMississippi.2004        -1.128150  0.173898 -6.4874 1.397e-10 ***      
                fesisNebraska.2012            0.600900  0.140305  4.2828 2.031e-05 ***      
                fesisNevada.2012             -0.690039  0.155438 -4.4393 1.007e-05 ***      
                fesisNevada.2019              0.902304  0.248387  3.6327 0.0002954 ***      
                fesisOregon.2004             -0.669301  0.172233 -3.8860 0.0001089 ***      
                fesisRhodeIsland.2005        -0.666868  0.161559 -4.1277 3.983e-05 ***      
                fesisSouthCarolina.2008       0.756364  0.141445  5.3474 1.116e-07 ***      
                fesisSouthDakota.2008         0.986700  0.156535  6.3034 4.435e-10 ***      
                fesisSouthDakota.2018        -0.767436  0.204875 -3.7459 0.0001905 ***      
                fesisTennessee.2005           0.467434  0.158796  2.9436 0.0033223 **       
                fesisWyoming.2003            -0.676889  0.200195 -3.3811 0.0007510 ***      
                fesisWyoming.2017            -0.676036  0.199279 -3.3924 0.0007211 ***      
                fesisWyoming.2020             1.604244  0.356598  4.4987 7.673e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                   Chi-sq df p-value      
                Ljung-Box AR(1)   0.91273  1  0.3394      
                Ljung-Box ARCH(1) 0.80321  1  0.3701      
                                                 
                SE of regression    0.30560      
                R-squared           0.94623      
                Log-lik.(n=1071) -194.03742      
us_q25

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 13:54:39 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 903       
                Sample: 1 to 903       
                      
                SPECIFIC mean equation:      
                      
                                             coef std.error  t-stat   p-value          
                lgdp                    -0.427275  1.273195 -0.3356 0.7372658          
                lpop                     0.780372  0.386722  2.0179 0.0439328 *        
                lgdp_sq                  0.018392  0.048006  0.3831 0.7017377          
                avg_temp                 0.021747  0.012042  1.8060 0.0712975 .        
                idArizona                1.530600  0.130577 11.7218 < 2.2e-16 ***      
                idCalifornia             2.281160  0.674286  3.3831 0.0007516 ***      
                idColorado               2.347635  0.244715  9.5933 < 2.2e-16 ***      
                idConnecticut            3.171897  0.259633 12.2168 < 2.2e-16 ***      
                idDelaware               3.030740  0.542654  5.5850 3.200e-08 ***      
                idDistrictofColumbia     2.041211  0.702584  2.9053 0.0037700 **       
                idFlorida                0.797662  0.442532  1.8025 0.0718425 .        
                idGeorgia                0.909559  0.244288  3.7233 0.0002104 ***      
                idHawaii                 0.017577  0.524051  0.0335 0.9732516          
                idIdaho                  1.544195  0.442737  3.4878 0.0005135 ***      
                idIllinois               1.578271  0.365292  4.3206 1.752e-05 ***      
                idIndiana                1.012716  0.195377  5.1834 2.760e-07 ***      
                idIowa                   0.909475  0.244232  3.7238 0.0002100 ***      
                idKansas                 0.560623  0.206485  2.7151 0.0067685 **       
                idKentucky               0.407937  0.125414  3.2527 0.0011908 **       
                idLouisiana              0.151279  0.142389  1.0624 0.2883579          
                idMaine                  1.434976  0.491760  2.9180 0.0036208 **       
                idMaryland               1.355532  0.176612  7.6752 4.799e-14 ***      
                idMassachusetts          2.860972  0.267231 10.7060 < 2.2e-16 ***      
                idMichigan               2.133120  0.334199  6.3828 2.940e-10 ***      
                idMinnesota              2.310446  0.294473  7.8460 1.371e-14 ***      
                idMissouri               0.785879  0.157277  4.9968 7.159e-07 ***      
                idNevada                 1.756236  0.270159  6.5007 1.404e-10 ***      
                idNewHampshire           2.385656  0.468647  5.0905 4.452e-07 ***      
                idNewJersey              1.734107  0.274306  6.3218 4.288e-10 ***      
                idNewMexico              1.924435  0.299963  6.4156 2.396e-10 ***      
                idNewYork                2.231443  0.528247  4.2242 2.673e-05 ***      
                idNorthCarolina          1.559981  0.241677  6.4548 1.874e-10 ***      
                idOhio                   1.901027  0.330740  5.7478 1.284e-08 ***      
                idOklahoma               0.786530  0.119882  6.5609 9.587e-11 ***      
                idOregon                 2.584335  0.250031 10.3361 < 2.2e-16 ***      
                idPennsylvania           1.910832  0.369169  5.1760 2.867e-07 ***      
                idRhodeIsland            2.403230  0.502532  4.7822 2.063e-06 ***      
                idSouthCarolina          1.234444  0.117267 10.5268 < 2.2e-16 ***      
                idSouthDakota            1.033361  0.637414  1.6212 0.1053726          
                idTennessee              0.332747  0.180924  1.8392 0.0662624 .        
                idTexas                  1.119919  0.538106  2.0812 0.0377301 *        
                idUtah                   1.628605  0.262422  6.2061 8.704e-10 ***      
                idVermont                1.974228  0.720366  2.7406 0.0062693 **       
                idVirginia               1.419175  0.228787  6.2030 8.865e-10 ***      
                idWashington             1.985601  0.269711  7.3620 4.497e-13 ***      
                idWisconsin              1.830146  0.265356  6.8969 1.078e-11 ***      
                time2000                -4.774105  8.365081 -0.5707 0.5683505          
                time2001                -4.729676  8.366992 -0.5653 0.5720428          
                time2002                -4.597846  8.370468 -0.5493 0.5829568          
                time2003                -4.541542  8.372540 -0.5424 0.5876710          
                time2004                -4.508321  8.377688 -0.5381 0.5906336          
                time2005                -4.305402  8.381836 -0.5137 0.6076322          
                time2006                -4.220808  8.385898 -0.5033 0.6148760          
                time2007                -4.046062  8.386201 -0.4825 0.6296062          
                time2008                -3.937372  8.384092 -0.4696 0.6387512          
                time2009                -3.771844  8.381994 -0.4500 0.6528366          
                time2010                -3.786068  8.385482 -0.4515 0.6517493          
                time2011                -3.844045  8.387913 -0.4583 0.6468727          
                time2012                -3.889339  8.392015 -0.4635 0.6431625          
                time2013                -3.908393  8.387555 -0.4660 0.6413597          
                time2014                -4.170427  8.389301 -0.4971 0.6192459          
                time2015                -4.163072  8.394493 -0.4959 0.6200804          
                time2016                -4.274788  8.396403 -0.5091 0.6108072          
                time2017                -4.298400  8.396665 -0.5119 0.6088496          
                time2018                -4.247210  8.397015 -0.5058 0.6131360          
                time2019                -4.408143  8.398045 -0.5249 0.5997970          
                time2020                -5.385429  8.398226 -0.6413 0.5215384          
                iis131                  -1.047177  0.287822 -3.6383 0.0002920 ***      
                iis135                  -1.528208  0.288524 -5.2966 1.525e-07 ***      
                iis136                  -0.867251  0.288349 -3.0076 0.0027151 **       
                iis137                  -0.929622  0.288355 -3.2239 0.0013158 **       
                iis205                  -0.900083  0.301349 -2.9868 0.0029045 **       
                iis207                  -1.414265  0.322567 -4.3844 1.318e-05 ***      
                iis208                  -1.699864  0.322505 -5.2708 1.747e-07 ***      
                iis315                   1.092499  0.286932  3.8075 0.0001511 ***      
                iis322                  -1.069214  0.285901 -3.7398 0.0001973 ***      
                iis362                  -0.803195  0.294399 -2.7283 0.0065064 **       
                iis368                  -0.777735  0.296291 -2.6249 0.0088324 **       
                iis464                  -1.029288  0.286408 -3.5938 0.0003458 ***      
                iis745                   0.834142  0.294823  2.8293 0.0047816 **       
                iis842                  -0.928714  0.286231 -3.2446 0.0012248 **       
                fesisConnecticut.2009   -0.564218  0.125969 -4.4790 8.587e-06 ***      
                fesisDelaware.2014      -0.907478  0.134987 -6.7227 3.386e-11 ***      
                fesisHawaii.2001         0.992731  0.296310  3.3503 0.0008449 ***      
                fesisHawaii.2009        -0.622438  0.151644 -4.1046 4.465e-05 ***      
                fesisHawaii.2016         0.659266  0.197912  3.3311 0.0009046 ***      
                fesisLouisiana.2011     -0.705815  0.164048 -4.3025 1.897e-05 ***      
                fesisLouisiana.2015      0.903712  0.181648  4.9751 7.983e-07 ***      
                fesisMaine.2011          0.390738  0.130901  2.9850 0.0029221 **       
                fesisNevada.2012        -0.749442  0.141776 -5.2861 1.612e-07 ***      
                fesisNevada.2019         0.972172  0.224647  4.3276 1.698e-05 ***      
                fesisOregon.2004        -0.672304  0.156701 -4.2904 2.002e-05 ***      
                fesisRhodeIsland.2005   -0.667374  0.146762 -4.5473 6.272e-06 ***      
                fesisSouthCarolina.2008  0.725444  0.127763  5.6781 1.905e-08 ***      
                fesisSouthDakota.2004    1.258291  0.312610  4.0251 6.235e-05 ***      
                fesisSouthDakota.2005   -1.391510  0.322443 -4.3155 1.791e-05 ***      
                fesisSouthDakota.2008    0.960490  0.191960  5.0036 6.918e-07 ***      
                fesisSouthDakota.2018   -0.635500  0.188004 -3.3802 0.0007592 ***      
                fesisTennessee.2005      0.465479  0.143341  3.2474 0.0012133 **       
                fesisUtah.2016          -0.457657  0.151604 -3.0188 0.0026184 **       
                fesisWisconsin.2014      0.455817  0.130529  3.4921 0.0005055 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                    Chi-sq df p-value      
                Ljung-Box AR(1)   0.017863  1  0.8937      
                Ljung-Box ARCH(1) 0.869265  1  0.3512      
                                                
                SE of regression   0.27552      
                R-squared          0.94648      
                Log-lik.(n=903)  -66.75849      

Patent Count

0.01

us_all

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 13:48:32 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1071       
                Sample: 1 to 1071       
                      
                SPECIFIC mean equation:      
                      
                                               coef   std.error   t-stat   p-value          
                lgdp                    -173.839647   23.743146  -7.3217 5.131e-13 ***      
                lpop                      21.517909    7.857243   2.7386 0.0062828 **       
                lgdp_sq                    6.286167    0.985121   6.3811 2.717e-10 ***      
                avg_temp                  -0.024337    0.244488  -0.0995 0.9207284          
                idAlaska                  -0.970332   15.503298  -0.0626 0.9501068          
                idArizona                 18.049776    2.816097   6.4095 2.273e-10 ***      
                idArkansas                -4.108178    3.868953  -1.0618 0.2885757          
                idCalifornia             116.355891   15.438775   7.5366 1.103e-13 ***      
                idColorado                32.041465    4.878563   6.5678 8.305e-11 ***      
                idConnecticut             52.849024    5.027212  10.5126 < 2.2e-16 ***      
                idDelaware                14.925191   11.313677   1.3192 0.1874074          
                idDistrictofColumbia      30.392283   14.682934   2.0699 0.0387249 *        
                idFlorida                 15.792479    9.246269   1.7080 0.0879586 .        
                idGeorgia                 12.269744    5.069713   2.4202 0.0156942 *        
                idHawaii                  -0.151160    9.028967  -0.0167 0.9866462          
                idIdaho                   -8.335227    9.189451  -0.9070 0.3646089          
                idIllinois                23.800302    7.443354   3.1975 0.0014309 **       
                idIndiana                  8.207571    3.974591   2.0650 0.0391867 *        
                idIowa                     5.259738    5.129192   1.0255 0.3054053          
                idKansas                   3.605216    4.428015   0.8142 0.4157394          
                idKentucky                 0.897098    2.760316   0.3250 0.7452522          
                idLouisiana                5.549265    2.638762   2.1030 0.0357240 *        
                idMaine                   -8.378734   10.273905  -0.8155 0.4149657          
                idMaryland                15.345951    3.517506   4.3627 1.422e-05 ***      
                idMassachusetts           48.932735    5.730490   8.5390 < 2.2e-16 ***      
                idMichigan                34.415710    6.766832   5.0859 4.388e-07 ***      
                idMinnesota               27.443237    5.864239   4.6798 3.279e-06 ***      
                idMississippi             -8.034347    3.791856  -2.1188 0.0343569 *        
                idMissouri                 6.016000    3.252983   1.8494 0.0647065 .        
                idMontana                -15.743007   12.006644  -1.3112 0.1901028          
                idNebraska                 3.009035    7.371508   0.4082 0.6832182          
                idNevada                   8.512748    5.304273   1.6049 0.1088439          
                idNewHampshire             4.654042    9.865143   0.4718 0.6371995          
                idNewJersey               26.507377    5.491436   4.8270 1.609e-06 ***      
                idNewMexico                4.489114    6.314296   0.7109 0.4772892          
                idNewYork                 66.373044   10.901539   6.0884 1.640e-09 ***      
                idNorthCarolina           23.403386    4.979711   4.6997 2.980e-06 ***      
                idNorthDakota            -17.981387   14.564243  -1.2346 0.2172683          
                idOhio                    32.489378    6.733945   4.8247 1.627e-06 ***      
                idOklahoma                 4.607253    2.689293   1.7132 0.0869976 .        
                idOregon                  15.471379    4.563059   3.3906 0.0007255 ***      
                idPennsylvania            25.783332    7.923748   3.2539 0.0011774 **       
                idRhodeIsland             -4.307630   10.558764  -0.4080 0.6833875          
                idSouthCarolina           18.465272    2.040843   9.0479 < 2.2e-16 ***      
                idSouthDakota            -10.661499   12.717169  -0.8384 0.4020376          
                idTennessee                6.583389    3.048079   2.1598 0.0310283 *        
                idTexas                   27.719805   11.277590   2.4580 0.0141467 *        
                idUtah                     6.861015    5.393363   1.2721 0.2036341          
                idVermont                -20.331350   14.923096  -1.3624 0.1733847          
                idVirginia                18.597458    4.597487   4.0451 5.644e-05 ***      
                idWashington              26.322530    5.325946   4.9423 9.088e-07 ***      
                idWestVirginia            -9.198380    7.170438  -1.2828 0.1998610          
                idWisconsin               19.471682    5.338433   3.6475 0.0002789 ***      
                idWyoming                 -6.805647   15.457943  -0.4403 0.6598405          
                time2000                 996.202193  161.750238   6.1589 1.071e-09 ***      
                time2001                 997.029124  161.821720   6.1613 1.055e-09 ***      
                time2002                 999.114728  161.862712   6.1726 9.851e-10 ***      
                time2003                 999.904189  161.865168   6.1774 9.568e-10 ***      
                time2004                1001.624355  161.926271   6.1857 9.097e-10 ***      
                time2005                1003.921371  161.993259   6.1973 8.474e-10 ***      
                time2006                1006.491736  162.088082   6.2095 7.863e-10 ***      
                time2007                1008.352621  162.090129   6.2209 7.333e-10 ***      
                time2008                1010.286096  162.061640   6.2340 6.770e-10 ***      
                time2009                1013.397190  162.094249   6.2519 6.063e-10 ***      
                time2010                1014.383437  162.172053   6.2550 5.949e-10 ***      
                time2011                1013.492433  162.210206   6.2480 6.209e-10 ***      
                time2012                1012.406314  162.290683   6.2382 6.594e-10 ***      
                time2013                1011.833543  162.155723   6.2399 6.528e-10 ***      
                time2014                1007.790921  162.171322   6.2144 7.634e-10 ***      
                time2015                1008.558828  162.281479   6.2149 7.610e-10 ***      
                time2016                1006.729553  162.340502   6.2013 8.267e-10 ***      
                time2017                1007.475374  162.332848   6.2062 8.024e-10 ***      
                time2018                1007.450832  162.290254   6.2077 7.951e-10 ***      
                time2019                1005.870319  162.268309   6.1988 8.396e-10 ***      
                time2020                 997.170380  162.367057   6.1415 1.190e-09 ***      
                iis85                    -72.253787    9.427735  -7.6640 4.356e-14 ***      
                iis86                    -46.745558    9.425537  -4.9595 8.340e-07 ***      
                iis87                    -54.388869    9.418837  -5.7745 1.038e-08 ***      
                iis88                    -53.507737    9.418476  -5.6811 1.767e-08 ***      
                iis89                    -24.778486    9.406539  -2.6342 0.0085682 **       
                iis92                     39.502726    7.457722   5.2969 1.457e-07 ***      
                iis93                     87.056601    7.450347  11.6849 < 2.2e-16 ***      
                iis94                    119.945499    7.460277  16.0779 < 2.2e-16 ***      
                iis95                     87.646053    7.469076  11.7345 < 2.2e-16 ***      
                iis96                     77.532533    7.474198  10.3734 < 2.2e-16 ***      
                iis97                     64.259629    7.461188   8.6125 < 2.2e-16 ***      
                iis98                     57.109061    7.437206   7.6788 3.905e-14 ***      
                iis105                  -140.895202    7.680583 -18.3443 < 2.2e-16 ***      
                iis450                    28.386999    7.109274   3.9930 7.017e-05 ***      
                iis693                   -34.933368    7.438931  -4.6960 3.034e-06 ***      
                fesisCalifornia.2006      79.794177    7.492126  10.6504 < 2.2e-16 ***      
                fesisCalifornia.2017     -41.262296    5.166510  -7.9865 3.906e-15 ***      
                fesisConnecticut.2013    -19.784585    3.033061  -6.5230 1.107e-10 ***      
                fesisMassachusetts.2006   32.722215    3.738906   8.7518 < 2.2e-16 ***      
                fesisMassachusetts.2014  -26.994156    3.575324  -7.5501 9.999e-14 ***      
                fesisNewYork.2016        -19.707860    3.840399  -5.1317 3.466e-07 ***      
                fesisNorthDakota.2012     18.916494    3.823981   4.9468 8.886e-07 ***      
                fesisPennsylvania.2007    29.265085    3.584766   8.1637 1.001e-15 ***      
                fesisPennsylvania.2014   -29.756674    3.577567  -8.3176 3.010e-16 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df   p-value          
                Ljung-Box AR(1)   192.37  1 < 2.2e-16 ***      
                Ljung-Box ARCH(1) 111.12  1 < 2.2e-16 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     6.58252      
                R-squared            0.96801      
                Log-lik.(n=1071) -3488.39465      
us_q25

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 0      
                      
                Date: Thu Mar 30 13:45:05 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 903       
                Sample: 1 to 903       
                      
                SPECIFIC mean equation:      
                      
                                               coef   std.error   t-stat   p-value          
                lgdp                    -182.850275   31.970587  -5.7193 1.502e-08 ***      
                lpop                      19.110037    9.142412   2.0903 0.0369044 *        
                lgdp_sq                    6.802014    1.273733   5.3402 1.206e-07 ***      
                avg_temp                   0.093003    0.317564   0.2929 0.7696998          
                idArizona                 17.626487    3.239533   5.4411 7.014e-08 ***      
                idCalifornia              98.794477   17.017273   5.8055 9.196e-09 ***      
                idColorado                32.679478    6.218307   5.2554 1.889e-07 ***      
                idConnecticut             54.735238    6.393786   8.5607 < 2.2e-16 ***      
                idDelaware                15.003421   12.927859   1.1605 0.2461658          
                idDistrictofColumbia      28.038900   16.853508   1.6637 0.0965611 .        
                idFlorida                 11.922706   10.684865   1.1158 0.2648160          
                idGeorgia                 10.280681    5.874206   1.7501 0.0804715 .        
                idHawaii                  -1.919989   10.614281  -0.1809 0.8565011          
                idIdaho                   -5.398139   10.999179  -0.4908 0.6237169          
                idIllinois                21.820998    8.856011   2.4640 0.0139465 *        
                idIndiana                  8.452473    4.903606   1.7237 0.0851375 .        
                idIowa                     6.659730    6.234370   1.0682 0.2857346          
                idKansas                   4.353254    5.155031   0.8445 0.3986569          
                idKentucky                 1.721074    3.283371   0.5242 0.6002969          
                idLouisiana                4.238518    3.088696   1.3723 0.1703585          
                idMaine                   -5.390085   12.252632  -0.4399 0.6601174          
                idMaryland                14.709351    4.320935   3.4042 0.0006961 ***      
                idMassachusetts           49.163618    7.083891   6.9402 8.003e-12 ***      
                idMichigan                34.955263    8.317829   4.2025 2.933e-05 ***      
                idMinnesota               28.548014    7.534282   3.7891 0.0001624 ***      
                idMissouri                 6.147282    3.953063   1.5551 0.1203190          
                idNevada                   9.666143    6.277342   1.5398 0.1239869          
                idNewHampshire             6.856838   11.604968   0.5909 0.5547827          
                idNewJersey               25.007477    6.640126   3.7661 0.0001778 ***      
                idNewMexico                5.870543    7.342619   0.7995 0.4242247          
                idNewYork                 63.010393   13.023121   4.8383 1.566e-06 ***      
                idNorthCarolina           22.114093    5.811056   3.8055 0.0001521 ***      
                idOhio                    31.593418    8.038750   3.9301 9.212e-05 ***      
                idOklahoma                 4.814022    3.051105   1.5778 0.1150015          
                idOregon                  17.030306    5.686169   2.9950 0.0028274 **       
                idPennsylvania            34.321850    8.998820   3.8140 0.0001471 ***      
                idRhodeIsland             -2.744730   12.274729  -0.2236 0.8231183          
                idSouthCarolina           18.524774    2.262977   8.1860 1.040e-15 ***      
                idSouthDakota             -8.645237   14.879163  -0.5810 0.5613814          
                idTennessee                6.323045    3.594446   1.7591 0.0789341 .        
                idTexas                   22.471872   13.072136   1.7191 0.0859829 .        
                idUtah                     8.461680    6.465795   1.3087 0.1910113          
                idVermont                -18.028665   17.596229  -1.0246 0.3058683          
                idVirginia                17.418336    5.521035   3.1549 0.0016646 **       
                idWashington              26.163185    6.714806   3.8963 0.0001057 ***      
                idWisconsin               20.799574    6.822792   3.0485 0.0023740 **       
                time2000                1042.161633  211.481975   4.9279 1.007e-06 ***      
                time2001                1042.837430  211.561414   4.9292 1.001e-06 ***      
                time2002                1045.122461  211.616906   4.9387 9.545e-07 ***      
                time2003                1045.850423  211.623079   4.9420 9.390e-07 ***      
                time2004                1047.366968  211.726450   4.9468 9.170e-07 ***      
                time2005                1050.189795  211.808935   4.9582 8.663e-07 ***      
                time2006                1052.203832  211.910577   4.9653 8.360e-07 ***      
                time2007                1055.192919  211.893983   4.9798 7.775e-07 ***      
                time2008                1057.656555  211.854660   4.9924 7.300e-07 ***      
                time2009                1061.763501  211.849857   5.0119 6.618e-07 ***      
                time2010                1062.718672  211.949214   5.0140 6.546e-07 ***      
                time2011                1061.297999  211.989502   5.0064 6.803e-07 ***      
                time2012                1059.997432  212.111145   4.9974 7.119e-07 ***      
                time2013                1059.333405  211.941940   4.9982 7.088e-07 ***      
                time2014                1053.787624  211.956062   4.9717 8.096e-07 ***      
                time2015                1054.433993  212.096983   4.9715 8.107e-07 ***      
                time2016                1052.199912  212.189885   4.9588 8.638e-07 ***      
                time2017                1053.035928  212.184308   4.9628 8.464e-07 ***      
                time2018                1052.922849  212.152420   4.9630 8.455e-07 ***      
                time2019                1051.037817  212.139813   4.9545 8.826e-07 ***      
                time2020                1040.858357  212.229766   4.9044 1.132e-06 ***      
                iis43                    -59.314945    9.066976  -6.5419 1.074e-10 ***      
                iis44                    -33.643106    9.064584  -3.7115 0.0002201 ***      
                iis45                    -41.525841    9.056938  -4.5850 5.255e-06 ***      
                iis46                    -40.851221    9.055618  -4.5111 7.398e-06 ***      
                iis49                     52.048613    8.729890   5.9621 3.710e-09 ***      
                iis50                     80.769158    8.696788   9.2872 < 2.2e-16 ***      
                iis51                    127.756629    8.686213  14.7080 < 2.2e-16 ***      
                iis52                    159.879698    8.718651  18.3377 < 2.2e-16 ***      
                iis53                    127.643583    8.707390  14.6592 < 2.2e-16 ***      
                iis54                    118.034056    8.703737  13.5613 < 2.2e-16 ***      
                iis55                    104.607262    8.672329  12.0622 < 2.2e-16 ***      
                iis56                     97.405106    8.633365  11.2824 < 2.2e-16 ***      
                iis57                     40.083329    8.670652   4.6229 4.401e-06 ***      
                iis58                     37.280664    8.569636   4.3503 1.532e-05 ***      
                iis59                     37.414748    8.545080   4.3785 1.351e-05 ***      
                iis63                   -139.356037    8.529358 -16.3384 < 2.2e-16 ***      
                iis408                    28.610827    7.894668   3.6241 0.0003080 ***      
                iis588                   -33.238217    8.261107  -4.0235 6.270e-05 ***      
                fesisCalifornia.2006      49.639768    7.093666   6.9978 5.440e-12 ***      
                fesisConnecticut.2009    -16.549613    3.310198  -4.9996 7.040e-07 ***      
                fesisMassachusetts.2006   30.563044    4.153326   7.3587 4.548e-13 ***      
                fesisMassachusetts.2014  -25.340111    3.966999  -6.3877 2.831e-10 ***      
                fesisNewYork.2016        -19.395846    4.265564  -4.5471 6.267e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                   Chi-sq df   p-value          
                Ljung-Box AR(1)   176.847  1 < 2.2e-16 ***      
                Ljung-Box ARCH(1)  70.157  1 < 2.2e-16 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     7.29534      
                R-squared            0.96537      
                Log-lik.(n=903)  -3030.77486      

AR1

Ihs Patent Count

0.01

us_all

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 14:04:36 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error   t-stat   p-value          
                ar1                            0.019074   0.028916   0.6596 0.5096505          
                lgdp                          50.380694   3.690418  13.6518 < 2.2e-16 ***      
                lpop                         -39.613917   2.273062 -17.4276 < 2.2e-16 ***      
                lgdp_sq                       -1.830075   0.220054  -8.3165 3.283e-16 ***      
                avg_temp                      -0.063897   0.089415  -0.7146 0.4750331          
                idAlaska                      -0.796288   0.174284  -4.5689 5.578e-06 ***      
                idArizona                      1.903561   0.130671  14.5676 < 2.2e-16 ***      
                idArkansas                     0.884278   0.380006   2.3270 0.0201833 *        
                idCalifornia                   4.173524   0.170702  24.4491 < 2.2e-16 ***      
                idColorado                     2.252950   0.135064  16.6807 < 2.2e-16 ***      
                idConnecticut                  2.893930   0.177418  16.3113 < 2.2e-16 ***      
                idDelaware                     1.757921   0.142069  12.3737 < 2.2e-16 ***      
                idDistrictofColumbia           0.216523   0.172481   1.2553 0.2096762          
                idFlorida                      2.345285   0.136321  17.2042 < 2.2e-16 ***      
                idGeorgia                      1.655659   0.127894  12.9456 < 2.2e-16 ***      
                idHawaii                       0.141390   0.122345   1.1557 0.2481241          
                idIdaho                        0.286037   0.117676   2.4307 0.0152610 *        
                idIllinois                     2.362110   0.136976  17.2447 < 2.2e-16 ***      
                idIndiana                      1.197654   0.122689   9.7617 < 2.2e-16 ***      
                idIowa                         0.272706   0.117625   2.3184 0.0206469 *        
                idKansas                      -0.019323   0.117321  -0.1647 0.8692158          
                idKentucky                     0.179184   0.118953   1.5063 0.1323274          
                idLouisiana                    0.113721   0.117414   0.9685 0.3330288          
                idMaine                        0.191079   0.118895   1.6071 0.1083725          
                idMaryland                     1.535412   0.125893  12.1962 < 2.2e-16 ***      
                idMassachusetts                3.038116   0.148278  20.4893 < 2.2e-16 ***      
                idMichigan                     2.572753   0.140442  18.3189 < 2.2e-16 ***      
                idMinnesota                    2.145976   0.134036  16.0104 < 2.2e-16 ***      
                idMississippi                 -1.227179   0.128317  -9.5637 < 2.2e-16 ***      
                idMissouri                     0.928943   0.121591   7.6399 5.502e-14 ***      
                idMontana                     -0.617057   0.118549  -5.2051 2.397e-07 ***      
                idNebraska                    -0.650784   0.145603  -4.4696 8.826e-06 ***      
                idNevada                       0.886146   0.120400   7.3600 4.111e-13 ***      
                idNewHampshire                 1.066159   0.122133   8.7295 < 2.2e-16 ***      
                idNewJersey                    2.236596   0.135136  16.5507 < 2.2e-16 ***      
                idNewMexico                    1.202397   0.122950   9.7796 < 2.2e-16 ***      
                idNewYork                      3.261397   0.152716  21.3560 < 2.2e-16 ***      
                idNorthCarolina                2.246451   0.135129  16.6245 < 2.2e-16 ***      
                idNorthDakota                 -0.757478   0.121757  -6.2212 7.514e-10 ***      
                idOhio                         2.579687   0.140929  18.3049 < 2.2e-16 ***      
                idOklahoma                     0.647998   0.118829   5.4532 6.376e-08 ***      
                idOregon                       1.706828   0.128090  13.3253 < 2.2e-16 ***      
                idPennsylvania                 2.641543   0.141661  18.6470 < 2.2e-16 ***      
                idRhodeIsland                  1.222128   0.206057   5.9310 4.273e-09 ***      
                idSouthCarolina                1.330287   0.167759   7.9297 6.414e-15 ***      
                idSouthDakota                 -0.994212   0.231375  -4.2970 1.918e-05 ***      
                idTennessee                    1.035226   0.122253   8.4679 < 2.2e-16 ***      
                idTexas                        2.789460   0.143887  19.3865 < 2.2e-16 ***      
                idUtah                         0.885998   0.120517   7.3517 4.360e-13 ***      
                idVermont                     -0.061984   0.117320  -0.5283 0.5973975          
                idVirginia                     1.845607   0.129610  14.2397 < 2.2e-16 ***      
                idWashington                   2.137756   0.133449  16.0193 < 2.2e-16 ***      
                idWestVirginia                -0.769000   0.119275  -6.4473 1.845e-10 ***      
                idWisconsin                    1.910537   0.130171  14.6771 < 2.2e-16 ***      
                idWyoming                     -0.441469   0.126854  -3.4801 0.0005249 ***      
                time2001                      -2.796206   0.575464  -4.8590 1.389e-06 ***      
                time2002                      -2.688232   0.533579  -5.0381 5.670e-07 ***      
                time2003                      -2.583384   0.462749  -5.5827 3.126e-08 ***      
                time2004                      -2.729814   0.329796  -8.2773 4.462e-16 ***      
                time2005                      -2.379763   0.253069  -9.4036 < 2.2e-16 ***      
                time2006                      -1.740122   0.203913  -8.5336 < 2.2e-16 ***      
                time2007                      -1.208997   0.177097  -6.8268 1.585e-11 ***      
                time2008                      -0.814112   0.217637  -3.7407 0.0001950 ***      
                time2009                      -0.114294   0.257257  -0.4443 0.6569458          
                time2010                      -0.065233   0.230503  -0.2830 0.7772398          
                time2011                       0.039727   0.168189   0.2362 0.8133275          
                time2012                       0.153991   0.153871   1.0008 0.3171987          
                time2013                      -0.047213   0.205264  -0.2300 0.8181352          
                time2014                      -0.206631   0.250061  -0.8263 0.4088372          
                time2015                       0.103765   0.120943   0.8580 0.3911371          
                time2016                       0.044282   0.109911   0.4029 0.6871214          
                iis17                         -1.187407   0.379672  -3.1275 0.0018193 **       
                iis75                         -1.459675   0.387977  -3.7623 0.0001791 ***      
                iis79                         -1.565092   0.388756  -4.0259 6.148e-05 ***      
                iis164                        -1.329543   0.399724  -3.3261 0.0009158 ***      
                iis168                        -1.211812   0.429861  -2.8191 0.0049207 **       
                iis235                        -1.699714   0.380613  -4.4657 8.982e-06 ***      
                iis237                        -1.575378   0.382148  -4.1224 4.092e-05 ***      
                iis238                        -1.791913   0.382284  -4.6874 3.190e-06 ***      
                iis346                        -1.469578   0.379484  -3.8726 0.0001154 ***      
                iis384                        -1.347022   0.379918  -3.5456 0.0004117 ***      
                iis481                         1.386250   0.381498   3.6337 0.0002950 ***      
                iis482                         2.027382   0.383003   5.2934 1.506e-07 ***      
                iis483                         1.780332   0.385157   4.6223 4.342e-06 ***      
                iis501                        -1.370882   0.379613  -3.6113 0.0003214 ***      
                iis548                        -1.111002   0.389964  -2.8490 0.0044848 **       
                iis687                        -1.197759   0.380949  -3.1441 0.0017198 **       
                iis829                         1.027913   0.386266   2.6612 0.0079245 **       
                iis839                        -1.628325   0.386425  -4.2138 2.761e-05 ***      
                iis843                        -1.246098   0.379553  -3.2831 0.0010660 **       
                iis1002                        1.203170   0.382050   3.1492 0.0016903 **       
                fesisAlaska.2007              -1.188477   0.207581  -5.7254 1.401e-08 ***      
                fesisAlaska.2014               0.768037   0.198037   3.8783 0.0001128 ***      
                fesisArkansas.2002            -1.556412   0.413664  -3.7625 0.0001790 ***      
                fesisArkansas.2006            -0.865953   0.282690  -3.0633 0.0022539 **       
                fesisArkansas.2009             1.518966   0.243887   6.2282 7.202e-10 ***      
                fesisConnecticut.2009         -0.605754   0.169841  -3.5666 0.0003805 ***      
                fesisDelaware.2014            -0.827115   0.183714  -4.5022 7.598e-06 ***      
                fesisDelaware.2020            -1.195272   0.399563  -2.9914 0.0028515 **       
                fesisDistrictofColumbia.2008  -0.680644   0.262891  -2.5891 0.0097770 **       
                fesisDistrictofColumbia.2012   0.980313   0.250622   3.9115 9.854e-05 ***      
                fesisMississippi.2020          1.526418   0.381401   4.0021 6.788e-05 ***      
                fesisNebraska.2012             0.774605   0.172102   4.5008 7.646e-06 ***      
                fesisRhodeIsland.2005         -0.896023   0.208246  -4.3027 1.870e-05 ***      
                fesisSouthCarolina.2008        0.823653   0.175107   4.7037 2.951e-06 ***      
                fesisSouthDakota.2004          1.689649   0.427221   3.9550 8.249e-05 ***      
                fesisSouthDakota.2005         -1.835290   0.427249  -4.2956 1.930e-05 ***      
                fesisSouthDakota.2008          1.198002   0.241569   4.9592 8.442e-07 ***      
                fesisWyoming.2017             -0.963831   0.235794  -4.0876 4.744e-05 ***      
                fesisWyoming.2020              1.948370   0.427297   4.5598 5.821e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                    Chi-sq df  p-value         
                Ljung-Box AR(1)   0.082864  1 0.773454         
                Ljung-Box ARCH(1) 7.193671  1 0.007316 **      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                 
                SE of regression    0.36611      
                R-squared           0.94128      
                Log-lik.(n=1020) -367.40855      
us_q25

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 14:08:43 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error   t-stat   p-value          
                ar1                            0.022307   0.029384   0.7592 0.4479895          
                lgdp                          58.680348   3.406874  17.2241 < 2.2e-16 ***      
                lpop                         -45.187852   2.068064 -21.8503 < 2.2e-16 ***      
                lgdp_sq                       -2.189357   0.203787 -10.7434 < 2.2e-16 ***      
                avg_temp                      -0.067006   0.082491  -0.8123 0.4168816          
                idArizona                      1.710551   0.119268  14.3421 < 2.2e-16 ***      
                idCalifornia                   3.973084   0.163415  24.3128 < 2.2e-16 ***      
                idColorado                     2.058891   0.124231  16.5731 < 2.2e-16 ***      
                idConnecticut                  2.726302   0.161495  16.8816 < 2.2e-16 ***      
                idDelaware                     1.572372   0.127918  12.2921 < 2.2e-16 ***      
                idDistrictofColumbia           0.065445   0.149165   0.4387 0.6609698          
                idFlorida                      2.150947   0.125644  17.1194 < 2.2e-16 ***      
                idGeorgia                      1.463389   0.116108  12.6036 < 2.2e-16 ***      
                idHawaii                       0.216373   0.134980   1.6030 0.1093480          
                idIdaho                        0.154023   0.105563   1.4591 0.1449587          
                idIllinois                     2.167629   0.126380  17.1517 < 2.2e-16 ***      
                idIndiana                      1.007063   0.110134   9.1439 < 2.2e-16 ***      
                idIowa                         0.032869   0.105509   0.3115 0.7554859          
                idKansas                      -0.267708   0.105111  -2.5469 0.0110638 *        
                idKentucky                    -0.011921   0.105238  -0.1133 0.9098424          
                idLouisiana                    0.040859   0.125800   0.3248 0.7454271          
                idMaine                        0.068117   0.106358   0.6405 0.5220700          
                idMaryland                     1.343730   0.113820  11.8057 < 2.2e-16 ***      
                idMassachusetts                2.841402   0.138951  20.4490 < 2.2e-16 ***      
                idMichigan                     2.377545   0.130257  18.2527 < 2.2e-16 ***      
                idMinnesota                    1.952152   0.123074  15.8617 < 2.2e-16 ***      
                idMissouri                     0.737769   0.108306   6.8119 1.954e-11 ***      
                idNevada                       0.905519   0.126969   7.1318 2.303e-12 ***      
                idNewHampshire                 0.875787   0.109491   7.9987 4.663e-15 ***      
                idNewJersey                    2.042521   0.124312  16.4306 < 2.2e-16 ***      
                idNewMexico                    1.011708   0.110435   9.1611 < 2.2e-16 ***      
                idNewYork                      3.063890   0.143837  21.3011 < 2.2e-16 ***      
                idNorthCarolina                2.052378   0.124304  16.5109 < 2.2e-16 ***      
                idOhio                         2.384381   0.130800  18.2293 < 2.2e-16 ***      
                idOklahoma                     0.459311   0.105647   4.3476 1.563e-05 ***      
                idOregon                       2.208360   0.208471  10.5931 < 2.2e-16 ***      
                idPennsylvania                 2.446090   0.131615  18.5852 < 2.2e-16 ***      
                idRhodeIsland                  1.153473   0.199597   5.7790 1.095e-08 ***      
                idSouthCarolina                1.163206   0.147577   7.8820 1.112e-14 ***      
                idSouthDakota                 -1.215874   0.150801  -8.0628 2.881e-15 ***      
                idTennessee                    0.843285   0.109105   7.7291 3.418e-14 ***      
                idTexas                        2.593570   0.134090  19.3420 < 2.2e-16 ***      
                idUtah                         0.696338   0.107616   6.4706 1.745e-10 ***      
                idVermont                     -0.248540   0.103861  -2.3930 0.0169515 *        
                idVirginia                     1.652871   0.118063  13.9999 < 2.2e-16 ***      
                idWashington                   1.944069   0.122411  15.8814 < 2.2e-16 ***      
                idWisconsin                    1.717655   0.118700  14.4705 < 2.2e-16 ***      
                time2001                      -3.473073   0.532592  -6.5211 1.270e-10 ***      
                time2002                      -3.284338   0.493697  -6.6525 5.496e-11 ***      
                time2003                      -3.210358   0.428535  -7.4915 1.887e-13 ***      
                time2004                      -3.213178   0.305544 -10.5162 < 2.2e-16 ***      
                time2005                      -2.848470   0.234188 -12.1632 < 2.2e-16 ***      
                time2006                      -2.196513   0.188401 -11.6587 < 2.2e-16 ***      
                time2007                      -1.611048   0.163427  -9.8579 < 2.2e-16 ***      
                time2008                      -1.154958   0.201543  -5.7306 1.441e-08 ***      
                time2009                      -0.354984   0.238375  -1.4892 0.1368513          
                time2010                      -0.210936   0.213996  -0.9857 0.3245935          
                time2011                      -0.156933   0.155912  -1.0066 0.3144697          
                time2012                       0.030394   0.142448   0.2134 0.8310976          
                time2013                      -0.130870   0.189812  -0.6895 0.4907335          
                time2014                      -0.291923   0.231105  -1.2632 0.2069179          
                time2015                       0.019224   0.111345   0.1726 0.8629725          
                time2016                      -0.026419   0.101611  -0.2600 0.7949288          
                iis2                          -1.167159   0.322839  -3.6153 0.0003197 ***      
                iis4                          -1.134984   0.322953  -3.5144 0.0004667 ***      
                iis10                         -1.178309   0.322706  -3.6513 0.0002787 ***      
                iis17                         -1.439717   0.322858  -4.4593 9.459e-06 ***      
                iis124                        -1.408405   0.338472  -4.1611 3.528e-05 ***      
                iis195                        -1.361019   0.331914  -4.1005 4.565e-05 ***      
                iis196                         1.270046   0.334075   3.8017 0.0001552 ***      
                iis197                        -1.284525   0.334250  -3.8430 0.0001317 ***      
                iis198                        -1.470641   0.333636  -4.4079 1.193e-05 ***      
                iis201                        -1.111691   0.321306  -3.4599 0.0005704 ***      
                iis262                         1.046270   0.322161   3.2477 0.0012145 **       
                iis306                        -1.389689   0.321113  -4.3277 1.707e-05 ***      
                iis344                        -1.451729   0.322082  -4.5073 7.595e-06 ***      
                iis350                        -1.173172   0.321950  -3.6440 0.0002867 ***      
                iis441                        -1.336241   0.321245  -4.1596 3.551e-05 ***      
                iis704                         1.684936   0.338272   4.9810 7.828e-07 ***      
                iis719                        -1.524994   0.330068  -4.6202 4.499e-06 ***      
                iis723                        -1.202645   0.321149  -3.7448 0.0001941 ***      
                fesisConnecticut.2009         -0.651559   0.144322  -4.5146 7.345e-06 ***      
                fesisDelaware.2014            -1.015329   0.148537  -6.8355 1.673e-11 ***      
                fesisDistrictofColumbia.2008  -1.261157   0.221871  -5.6842 1.871e-08 ***      
                fesisDistrictofColumbia.2011   1.451934   0.207939   6.9825 6.312e-12 ***      
                fesisHawaii.2009              -0.620323   0.157305  -3.9434 8.772e-05 ***      
                fesisKansas.2020               1.237235   0.321244   3.8514 0.0001273 ***      
                fesisLouisiana.2011           -0.845072   0.186735  -4.5255 6.986e-06 ***      
                fesisLouisiana.2015            1.027650   0.203398   5.0524 5.464e-07 ***      
                fesisNevada.2012              -0.713406   0.152519  -4.6775 3.435e-06 ***      
                fesisNevada.2019               1.120575   0.251053   4.4635 9.279e-06 ***      
                fesisOregon.2004              -0.816302   0.197244  -4.1385 3.884e-05 ***      
                fesisRhodeIsland.2004         -0.897726   0.198936  -4.5126 7.412e-06 ***      
                fesisRhodeIsland.2019         -0.736436   0.236218  -3.1176 0.0018917 **       
                fesisSouthCarolina.2008        0.784104   0.148528   5.2792 1.693e-07 ***      
                fesisSouthDakota.2008          1.726160   0.222922   7.7433 3.080e-14 ***      
                fesisSouthDakota.2011         -0.754777   0.208796  -3.6149 0.0003202 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                     Chi-sq df p-value      
                Ljung-Box AR(1)   0.0031803  1  0.9550      
                Ljung-Box ARCH(1) 1.9306558  1  0.1647      
                                                 
                SE of regression    0.30923      
                R-squared           0.94548      
                Log-lik.(n=860)  -162.42030      

0.05

us_all

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 14:04:40 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error   t-stat   p-value          
                ar1                            0.010941   0.026082   0.4195 0.6749635          
                lgdp                          53.327528   3.233205  16.4937 < 2.2e-16 ***      
                lpop                         -41.365939   1.983414 -20.8559 < 2.2e-16 ***      
                lgdp_sq                       -1.936686   0.192007 -10.0865 < 2.2e-16 ***      
                avg_temp                      -0.154836   0.077038  -2.0099 0.0447571 *        
                idAlaska                      -0.231492   0.258842  -0.8943 0.3713917          
                idArizona                      2.642537   0.235573  11.2175 < 2.2e-16 ***      
                idArkansas                     1.366884   0.309439   4.4173 1.127e-05 ***      
                idCalifornia                   4.931192   0.255462  19.3030 < 2.2e-16 ***      
                idColorado                     2.994564   0.237566  12.6052 < 2.2e-16 ***      
                idConnecticut                  3.646513   0.256408  14.2215 < 2.2e-16 ***      
                idDelaware                     2.494535   0.239815  10.4019 < 2.2e-16 ***      
                idDistrictofColumbia           0.942524   0.252011   3.7400 0.0001962 ***      
                idFlorida                      3.087603   0.238145  12.9652 < 2.2e-16 ***      
                idGeorgia                      2.392773   0.234340  10.2107 < 2.2e-16 ***      
                idHawaii                       1.104609   0.244325   4.5211 7.013e-06 ***      
                idIdaho                       -0.136241   0.377284  -0.3611 0.7181058          
                idIllinois                     3.104788   0.238449  13.0207 < 2.2e-16 ***      
                idIndiana                      1.930542   0.232089   8.3181 3.471e-16 ***      
                idIowa                         0.098346   0.377286   0.2607 0.7944122          
                idKansas                       0.800703   0.232657   3.4416 0.0006062 ***      
                idKentucky                     0.902225   0.230447   3.9151 9.750e-05 ***      
                idLouisiana                    0.940935   0.239671   3.9259 9.329e-05 ***      
                idMaine                        0.784769   0.244350   3.2117 0.0013686 **       
                idMaryland                     2.271047   0.233466   9.7275 < 2.2e-16 ***      
                idMassachusetts                3.786413   0.243857  15.5272 < 2.2e-16 ***      
                idMichigan                     3.317259   0.240074  13.8177 < 2.2e-16 ***      
                idMinnesota                    2.887000   0.237095  12.1765 < 2.2e-16 ***      
                idMississippi                 -0.209058   0.254126  -0.8227 0.4109323          
                idMissouri                     1.661872   0.231785   7.1699 1.615e-12 ***      
                idMontana                      0.049370   0.230955   0.2138 0.8307804          
                idNebraska                     0.862260   0.377521   2.2840 0.0226134 *        
                idNevada                       1.815742   0.239831   7.5709 9.531e-14 ***      
                idNewHampshire                 1.798500   0.231854   7.7570 2.452e-14 ***      
                idNewJersey                    2.978251   0.237599  12.5348 < 2.2e-16 ***      
                idNewMexico                    1.935533   0.232200   8.3356 3.027e-16 ***      
                idNewYork                      4.011687   0.246064  16.3034 < 2.2e-16 ***      
                idNorthCarolina                2.988102   0.237596  12.5764 < 2.2e-16 ***      
                idNorthDakota                 -0.181824   0.258853  -0.7024 0.4826056          
                idOhio                         3.324441   0.240305  13.8343 < 2.2e-16 ***      
                idOklahoma                     1.376099   0.230477   5.9707 3.451e-09 ***      
                idOregon                       2.444079   0.234427  10.4258 < 2.2e-16 ***      
                idPennsylvania                 3.386666   0.240652  14.0729 < 2.2e-16 ***      
                idRhodeIsland                  1.925693   0.268778   7.1646 1.674e-12 ***      
                idSouthCarolina                2.066010   0.250341   8.2528 5.771e-16 ***      
                idSouthDakota                 -0.228190   0.258900  -0.8814 0.3783567          
                idTennessee                    1.764967   0.231817   7.6136 6.996e-14 ***      
                idTexas                        3.535682   0.241718  14.6273 < 2.2e-16 ***      
                idUtah                         1.616545   0.231175   6.9927 5.405e-12 ***      
                idVermont                      0.737011   0.244842   3.0102 0.0026873 **       
                idVirginia                     1.496078   0.379694   3.9402 8.799e-05 ***      
                idWashington                   2.878436   0.236827  12.1541 < 2.2e-16 ***      
                idWestVirginia                 0.177580   0.236762   0.7500 0.4534370          
                idWisconsin                    2.649191   0.235350  11.2564 < 2.2e-16 ***      
                idWyoming                      0.352556   0.232440   1.5168 0.1296926          
                time2001                      -2.996700   0.499419  -6.0004 2.896e-09 ***      
                time2002                      -2.824583   0.463551  -6.0934 1.665e-09 ***      
                time2003                      -2.892503   0.401517  -7.2039 1.276e-12 ***      
                time2004                      -2.962454   0.286930 -10.3247 < 2.2e-16 ***      
                time2005                      -2.679745   0.220103 -12.1750 < 2.2e-16 ***      
                time2006                      -1.909146   0.178102 -10.7194 < 2.2e-16 ***      
                time2007                      -1.368130   0.154215  -8.8716 < 2.2e-16 ***      
                time2008                      -1.077149   0.187964  -5.7306 1.383e-08 ***      
                time2009                      -0.341627   0.222091  -1.5382 0.1243595          
                time2010                      -0.244407   0.198897  -1.2288 0.2194759          
                time2011                      -0.077996   0.145904  -0.5346 0.5930867          
                time2012                       0.137050   0.133285   1.0283 0.3041192          
                time2013                      -0.215701   0.176704  -1.2207 0.2225379          
                time2014                      -0.453714   0.214903  -2.1112 0.0350386 *        
                time2015                       0.069528   0.103976   0.6687 0.5038669          
                time2016                       0.068111   0.095061   0.7165 0.4738738          
                iis4                          -1.194503   0.321385  -3.7167 0.0002148 ***      
                iis10                         -1.241798   0.321091  -3.8674 0.0001183 ***      
                iis17                         -1.460328   0.321446  -4.5430 6.336e-06 ***      
                iis23                          0.871269   0.339974   2.5628 0.0105534 *        
                iis62                         -1.885034   0.382873  -4.9234 1.019e-06 ***      
                iis63                         -1.594420   0.380000  -4.1958 3.000e-05 ***      
                iis64                         -1.626769   0.380005  -4.2809 2.070e-05 ***      
                iis66                         -1.805881   0.328147  -5.5033 4.918e-08 ***      
                iis67                         -1.479730   0.328401  -4.5059 7.522e-06 ***      
                iis68                         -1.469739   0.327655  -4.4856 8.254e-06 ***      
                iis75                         -1.553012   0.326972  -4.7497 2.386e-06 ***      
                iis77                         -1.042545   0.327518  -3.1832 0.0015090 **       
                iis79                         -1.617845   0.327888  -4.9341 9.662e-07 ***      
                iis164                        -1.344912   0.335303  -4.0110 6.570e-05 ***      
                iis168                        -1.161611   0.360842  -3.2192 0.0013337 **       
                iis235                        -1.349813   0.328917  -4.1038 4.450e-05 ***      
                iis236                         1.262582   0.330634   3.8187 0.0001438 ***      
                iis237                        -1.215294   0.330841  -3.6733 0.0002542 ***      
                iis238                        -1.498371   0.330353  -4.5357 6.555e-06 ***      
                iis322                        -0.980052   0.319980  -3.0629 0.0022605 **       
                iis326                        -0.923241   0.319890  -2.8861 0.0039976 **       
                iis331                        -1.049045   0.319753  -3.2808 0.0010767 **       
                iis346                        -1.447706   0.318412  -4.5466 6.230e-06 ***      
                iis379                         0.825636   0.339785   2.4299 0.0153072 *        
                iis384                        -1.235789   0.329149  -3.7545 0.0001853 ***      
                iis390                        -1.291813   0.325413  -3.9698 7.794e-05 ***      
                iis481                         1.029056   0.335289   3.0692 0.0022138 **       
                iis482                         1.664551   0.335980   4.9543 8.736e-07 ***      
                iis483                         1.512428   0.337307   4.4838 8.322e-06 ***      
                iis493                        -0.677770   0.326873  -2.0735 0.0384224 *        
                iis501                        -1.429499   0.318588  -4.4870 8.203e-06 ***      
                iis531                         1.031504   0.318324   3.2404 0.0012393 **       
                iis548                        -1.406792   0.342128  -4.1119 4.300e-05 ***      
                iis550                        -1.215360   0.339931  -3.5753 0.0003693 ***      
                iis578                        -0.814970   0.335150  -2.4317 0.0152327 *        
                iis687                        -1.120162   0.325429  -3.4421 0.0006050 ***      
                iis691                        -0.982037   0.324011  -3.0309 0.0025114 **       
                iis817                         0.652858   0.322975   2.0214 0.0435482 *        
                iis824                         1.625295   0.339889   4.7818 2.042e-06 ***      
                iis826                        -0.710780   0.339918  -2.0910 0.0368175 *        
                iis829                         1.019642   0.328870   3.1004 0.0019952 **       
                iis837                         0.648232   0.329459   1.9676 0.0494386 *        
                iis839                        -1.074236   0.379904  -2.8276 0.0047978 **       
                iis843                        -1.224507   0.318358  -3.8463 0.0001287 ***      
                iis902                        -1.062725   0.329134  -3.2289 0.0012899 **       
                iis973                        -0.871061   0.336273  -2.5903 0.0097500 **       
                iis976                        -0.761556   0.334963  -2.2736 0.0232379 *        
                fesisAlabama.2003              0.999479   0.234823   4.2563 2.306e-05 ***      
                fesisAlabama.2020             -0.822472   0.322538  -2.5500 0.0109444 *        
                fesisAlaska.2007              -1.041748   0.183687  -5.6713 1.934e-08 ***      
                fesisAlaska.2014               0.769432   0.166191   4.6298 4.223e-06 ***      
                fesisArkansas.2006            -0.570626   0.242976  -2.3485 0.0190747 *        
                fesisConnecticut.2009         -0.619621   0.142865  -4.3371 1.614e-05 ***      
                fesisDelaware.2014            -0.835838   0.154493  -5.4102 8.161e-08 ***      
                fesisDelaware.2020            -1.154875   0.335277  -3.4445 0.0005996 ***      
                fesisDistrictofColumbia.2008  -0.694550   0.220761  -3.1462 0.0017111 **       
                fesisDistrictofColumbia.2012   0.991412   0.210622   4.7071 2.927e-06 ***      
                fesisHawaii.2009              -0.591271   0.155839  -3.7941 0.0001585 ***      
                fesisIdaho.2002                1.208043   0.318680   3.7908 0.0001606 ***      
                fesisIowa.2002                 1.839494   0.439033   4.1899 3.079e-05 ***      
                fesisIowa.2003                -0.942205   0.319772  -2.9465 0.0033006 **       
                fesisKansas.2020               1.004970   0.320089   3.1397 0.0017491 **       
                fesisLouisiana.2011           -0.829189   0.184787  -4.4873 8.192e-06 ***      
                fesisLouisiana.2015            0.900718   0.209212   4.3053 1.859e-05 ***      
                fesisMaine.2010                0.343333   0.148065   2.3188 0.0206395 *        
                fesisMississippi.2010         -0.412281   0.164606  -2.5047 0.0124408 *        
                fesisMississippi.2020          1.669431   0.327217   5.1019 4.137e-07 ***      
                fesisNebraska.2002            -1.338563   0.358413  -3.7347 0.0002003 ***      
                fesisNebraska.2005             0.882262   0.226795   3.8901 0.0001079 ***      
                fesisNebraska.2012             0.455331   0.189684   2.4005 0.0165850 *        
                fesisNebraska.2018            -0.986363   0.335415  -2.9407 0.0033620 **       
                fesisNebraska.2019             1.397238   0.380204   3.6750 0.0002526 ***      
                fesisNevada.2012              -0.567551   0.158555  -3.5795 0.0003635 ***      
                fesisNevada.2019               0.969530   0.253414   3.8259 0.0001397 ***      
                fesisNorthDakota.2006          1.122952   0.340254   3.3003 0.0010054 **       
                fesisNorthDakota.2007         -1.006774   0.324425  -3.1033 0.0019764 **       
                fesisNorthDakota.2020          0.958434   0.324278   2.9556 0.0032057 **       
                fesisRhodeIsland.2005         -0.865793   0.175075  -4.9453 9.141e-07 ***      
                fesisSouthCarolina.2008        0.777576   0.149219   5.2110 2.352e-07 ***      
                fesisSouthDakota.2008          1.044951   0.179016   5.8372 7.512e-09 ***      
                fesisSouthDakota.2018         -0.556060   0.245793  -2.2623 0.0239261 *        
                fesisVermont.2010              0.646835   0.210450   3.0736 0.0021817 **       
                fesisVermont.2013             -0.947193   0.210535  -4.4990 7.764e-06 ***      
                fesisVirginia.2002             1.145069   0.318663   3.5934 0.0003449 ***      
                fesisWestVirginia.2013        -0.370516   0.156497  -2.3676 0.0181260 *        
                fesisWyoming.2017             -1.048488   0.197166  -5.3178 1.339e-07 ***      
                fesisWyoming.2020              1.991781   0.358521   5.5556 3.688e-08 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                    Chi-sq df p-value      
                Ljung-Box AR(1)   0.098093  1  0.7541      
                Ljung-Box ARCH(1) 1.746387  1  0.1863      
                                                 
                SE of regression    0.30691      
                R-squared           0.96091      
                Log-lik.(n=1020) -163.50330      
us_q25

                Formula: ihs_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 14:08:41 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error   t-stat   p-value          
                ar1                            0.036918   0.027453   1.3448 0.1791021          
                lgdp                          55.202445   3.168572  17.4219 < 2.2e-16 ***      
                lpop                         -43.175827   1.932948 -22.3368 < 2.2e-16 ***      
                lgdp_sq                       -2.008385   0.189143 -10.6183 < 2.2e-16 ***      
                avg_temp                      -0.105989   0.076442  -1.3865 0.1660004          
                idArizona                      2.580060   0.218061  11.8318 < 2.2e-16 ***      
                idCalifornia                   4.809013   0.241289  19.9305 < 2.2e-16 ***      
                idColorado                     2.923662   0.220395  13.2656 < 2.2e-16 ***      
                idConnecticut                  3.570940   0.238943  14.9447 < 2.2e-16 ***      
                idDelaware                     2.443994   0.221736  11.0221 < 2.2e-16 ***      
                idDistrictofColumbia           0.950862   0.231736   4.1032 4.524e-05 ***      
                idFlorida                      3.014453   0.221074  13.6355 < 2.2e-16 ***      
                idGeorgia                      2.336244   0.216618  10.7851 < 2.2e-16 ***      
                idHawaii                       1.102116   0.224711   4.9046 1.150e-06 ***      
                idIdaho                        1.053320   0.212416   4.9588 8.792e-07 ***      
                idIllinois                     3.030489   0.221430  13.6860 < 2.2e-16 ***      
                idIndiana                      1.887508   0.213996   8.8203 < 2.2e-16 ***      
                idIowa                         0.071556   0.346800   0.2063 0.8365880          
                idKansas                       0.783109   0.214102   3.6576 0.0002725 ***      
                idKentucky                    -0.100833   0.347040  -0.2906 0.7714756          
                idLouisiana                    0.932828   0.220475   4.2310 2.617e-05 ***      
                idMaine                        0.963846   0.212536   4.5350 6.712e-06 ***      
                idMaryland                     2.219241   0.215597  10.2935 < 2.2e-16 ***      
                idMassachusetts                3.694167   0.227762  16.2194 < 2.2e-16 ***      
                idMichigan                     3.237120   0.223334  14.4946 < 2.2e-16 ***      
                idMinnesota                    2.817983   0.219843  12.8182 < 2.2e-16 ***      
                idMissouri                     1.628938   0.213492   7.6300 7.187e-14 ***      
                idNevada                       1.783865   0.221072   8.0692 2.832e-15 ***      
                idNewHampshire                 1.757217   0.213723   8.2219 8.882e-16 ***      
                idNewJersey                    2.907218   0.220433  13.1886 < 2.2e-16 ***      
                idNewMexico                    1.891708   0.214124   8.8346 < 2.2e-16 ***      
                idNewYork                      3.913074   0.230343  16.9880 < 2.2e-16 ***      
                idNorthCarolina                2.917082   0.220430  13.2336 < 2.2e-16 ***      
                idOhio                         3.243510   0.223604  14.5056 < 2.2e-16 ***      
                idOklahoma                     1.348356   0.212147   6.3558 3.611e-10 ***      
                idOregon                       2.773528   0.291886   9.5021 < 2.2e-16 ***      
                idPennsylvania                 3.304556   0.224011  14.7518 < 2.2e-16 ***      
                idRhodeIsland                  1.997230   0.259779   7.6882 4.721e-14 ***      
                idSouthCarolina                2.028414   0.230888   8.7853 < 2.2e-16 ***      
                idSouthDakota                 -0.205429   0.238314  -0.8620 0.3889581          
                idTennessee                    1.727619   0.213556   8.0898 2.424e-15 ***      
                idTexas                        3.450062   0.225259  15.3160 < 2.2e-16 ***      
                idUtah                         1.633224   0.213383   7.6540 6.046e-14 ***      
                idVermont                      0.291812   0.245428   1.1890 0.2348218          
                idVirginia                     1.425304   0.349782   4.0748 5.099e-05 ***      
                idWashington                   2.810518   0.219530  12.8025 < 2.2e-16 ***      
                idWisconsin                    2.587742   0.217799  11.8813 < 2.2e-16 ***      
                time2001                      -3.028662   0.494552  -6.1241 1.476e-09 ***      
                time2002                      -2.941788   0.458148  -6.4210 2.410e-10 ***      
                time2003                      -2.941720   0.397904  -7.3930 3.866e-13 ***      
                time2004                      -2.998422   0.283581 -10.5734 < 2.2e-16 ***      
                time2005                      -2.708109   0.217311 -12.4619 < 2.2e-16 ***      
                time2006                      -2.030931   0.174932 -11.6099 < 2.2e-16 ***      
                time2007                      -1.504339   0.151385  -9.9371 < 2.2e-16 ***      
                time2008                      -1.103453   0.186972  -5.9017 5.461e-09 ***      
                time2009                      -0.314542   0.221419  -1.4206 0.1558601          
                time2010                      -0.211875   0.198756  -1.0660 0.2867665          
                time2011                      -0.098704   0.144727  -0.6820 0.4954501          
                time2012                       0.089286   0.131688   0.6780 0.4979753          
                time2013                      -0.162958   0.176137  -0.9252 0.3551705          
                time2014                      -0.368080   0.214809  -1.7135 0.0870325 .        
                time2015                       0.061194   0.102842   0.5950 0.5520062          
                time2016                       0.022343   0.093660   0.2386 0.8115165          
                iis4                          -1.232858   0.295795  -4.1679 3.435e-05 ***      
                iis10                         -1.244649   0.295518  -4.2118 2.844e-05 ***      
                iis17                         -1.512481   0.295800  -5.1132 4.031e-07 ***      
                iis124                        -1.400003   0.308637  -4.5361 6.678e-06 ***      
                iis128                        -0.962299   0.353188  -2.7246 0.0065886 **       
                iis195                        -1.363687   0.302654  -4.5058 7.677e-06 ***      
                iis196                         1.287119   0.304737   4.2237 2.701e-05 ***      
                iis197                        -1.284004   0.304926  -4.2109 2.855e-05 ***      
                iis198                        -1.475157   0.304367  -4.8466 1.529e-06 ***      
                iis201                        -1.218348   0.293365  -4.1530 3.661e-05 ***      
                iis262                         1.005852   0.294409   3.4165 0.0006687 ***      
                iis282                        -0.930508   0.294416  -3.1605 0.0016386 **       
                iis286                        -0.876272   0.294309  -2.9774 0.0030014 **       
                iis291                        -1.035634   0.294122  -3.5211 0.0004559 ***      
                iis306                        -1.459150   0.293357  -4.9740 8.149e-07 ***      
                iis339                         0.788137   0.312781   2.5198 0.0119512 *        
                iis344                        -1.443380   0.293712  -4.9143 1.096e-06 ***      
                iis350                        -1.149642   0.293575  -3.9160 9.829e-05 ***      
                iis441                        -1.446875   0.293304  -4.9330 9.992e-07 ***      
                iis478                        -0.821642   0.308381  -2.6644 0.0078801 **       
                iis622                         0.783725   0.350106   2.2385 0.0254806 *        
                iis704                         1.584416   0.312828   5.0648 5.158e-07 ***      
                iis706                        -0.689560   0.312759  -2.2048 0.0277756 *        
                iis714                         0.868268   0.305023   2.8466 0.0045408 **       
                iis717                         0.973697   0.305407   3.1882 0.0014915 **       
                iis719                        -1.317940   0.305446  -4.3148 1.813e-05 ***      
                iis723                        -1.206159   0.292858  -4.1186 4.239e-05 ***      
                iis779                        -1.044691   0.293037  -3.5650 0.0003870 ***      
                fesisAlabama.2003              0.992479   0.216170   4.5912 5.172e-06 ***      
                fesisAlabama.2020             -0.828707   0.296966  -2.7906 0.0053959 **       
                fesisConnecticut.2009         -0.625936   0.131733  -4.7516 2.422e-06 ***      
                fesisDelaware.2014            -0.845443   0.142484  -5.9336 4.538e-09 ***      
                fesisDelaware.2020            -1.109472   0.308417  -3.5973 0.0003428 ***      
                fesisDistrictofColumbia.2008  -0.897686   0.235061  -3.8190 0.0001452 ***      
                fesisDistrictofColumbia.2011   1.097889   0.225183   4.8755 1.327e-06 ***      
                fesisHawaii.2009              -0.596704   0.143534  -4.1572 3.596e-05 ***      
                fesisIowa.2002                 0.902776   0.293864   3.0721 0.0022030 **       
                fesisKansas.2020               1.039805   0.294448   3.5314 0.0004388 ***      
                fesisKentucky.2002             1.040586   0.293895   3.5407 0.0004239 ***      
                fesisLouisiana.2011           -0.819949   0.170374  -4.8126 1.804e-06 ***      
                fesisLouisiana.2015            0.868540   0.192774   4.5055 7.686e-06 ***      
                fesisNevada.2012              -0.573974   0.146131  -3.9278 9.368e-05 ***      
                fesisNevada.2019               0.969593   0.233195   4.1579 3.586e-05 ***      
                fesisOregon.2004              -0.500711   0.215070  -2.3281 0.0201719 *        
                fesisRhodeIsland.2004         -0.840420   0.181565  -4.6288 4.339e-06 ***      
                fesisRhodeIsland.2019         -0.764348   0.215509  -3.5467 0.0004145 ***      
                fesisSouthCarolina.2008        0.792270   0.135583   5.8434 7.643e-09 ***      
                fesisSouthDakota.2008          1.634486   0.210046   7.7815 2.394e-14 ***      
                fesisSouthDakota.2011         -0.977298   0.197051  -4.9596 8.754e-07 ***      
                fesisVermont.2005              0.770514   0.175763   4.3838 1.334e-05 ***      
                fesisVermont.2013             -0.645222   0.143352  -4.5010 7.847e-06 ***      
                fesisVirginia.2002             1.156122   0.293350   3.9411 8.874e-05 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                   Chi-sq df p-value      
                Ljung-Box AR(1)   0.11978  1  0.7293      
                Ljung-Box ARCH(1) 2.16877  1  0.1408      
                                                
                SE of regression   0.28194      
                R-squared          0.95575      
                Log-lik.(n=860)  -73.98639      

Log Patent Count

0.01

us_all

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 13:55:59 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                                    coef   std.error   t-stat   p-value          
                ar1                            0.0340103   0.0292850   1.1614 0.2458010          
                lgdp                          43.7263263   3.0635825  14.2729 < 2.2e-16 ***      
                lpop                         -34.6166241   1.8818116 -18.3954 < 2.2e-16 ***      
                lgdp_sq                       -1.5677954   0.1825802  -8.5869 < 2.2e-16 ***      
                avg_temp                      -0.0751846   0.0745140  -1.0090 0.3132418          
                idAlaska                      -0.5180913   0.1441149  -3.5950 0.0003418 ***      
                idArizona                      1.6678845   0.1086957  15.3445 < 2.2e-16 ***      
                idArkansas                     0.7656132   0.3161752   2.4215 0.0156513 *        
                idCalifornia                   3.8523607   0.1508034  25.5456 < 2.2e-16 ***      
                idColorado                     1.9961434   0.1131794  17.6370 < 2.2e-16 ***      
                idConnecticut                  2.6023154   0.1498965  17.3608 < 2.2e-16 ***      
                idDelaware                     1.5350347   0.1179889  13.0100 < 2.2e-16 ***      
                idDistrictofColumbia           0.2349892   0.1429508   1.6438 0.1005521          
                idFlorida                      2.0823362   0.1144555  18.1934 < 2.2e-16 ***      
                idGeorgia                      1.4373713   0.1059295  13.5691 < 2.2e-16 ***      
                idHawaii                       0.3487364   0.1283772   2.7165 0.0067224 **       
                idIdaho                        0.2628188   0.0967373   2.7168 0.0067157 **       
                idIllinois                     2.0965592   0.1151018  18.2148 < 2.2e-16 ***      
                idIndiana                      1.0225522   0.1009613  10.1282 < 2.2e-16 ***      
                idIowa                         0.2504755   0.0966991   2.5903 0.0097433 **       
                idKansas                       0.0221685   0.0965109   0.2297 0.8183767          
                idKentucky                     0.1779708   0.0978497   1.8188 0.0692667 .        
                idLouisiana                    0.1248774   0.0965517   1.2934 0.1962092          
                idMaine                        0.1370113   0.0965157   1.4196 0.1560725          
                idMaryland                     1.3247738   0.1039667  12.7423 < 2.2e-16 ***      
                idMassachusetts                2.7456516   0.1269424  21.6291 < 2.2e-16 ***      
                idMichigan                     2.3006979   0.1187293  19.3777 < 2.2e-16 ***      
                idMinnesota                    1.8942056   0.1120803  16.9004 < 2.2e-16 ***      
                idMississippi                  0.4695245   0.1905292   2.4643 0.0139107 *        
                idMissouri                     0.7867603   0.0999601   7.8707 9.956e-15 ***      
                idMontana                     -0.4235795   0.0974812  -4.3452 1.547e-05 ***      
                idNebraska                    -0.4476276   0.1201317  -3.7261 0.0002064 ***      
                idNevada                       0.9204212   0.1183915   7.7744 2.040e-14 ***      
                idNewHampshire                 0.9067645   0.1004430   9.0277 < 2.2e-16 ***      
                idNewJersey                    1.9782158   0.1132114  17.4736 < 2.2e-16 ***      
                idNewMexico                    1.0264644   0.1011903  10.1439 < 2.2e-16 ***      
                idNewYork                      2.9616957   0.1316362  22.4991 < 2.2e-16 ***      
                idNorthCarolina                1.9879208   0.1132110  17.5594 < 2.2e-16 ***      
                idNorthDakota                 -0.5278500   0.1000470  -5.2760 1.650e-07 ***      
                idOhio                         2.3052030   0.1192060  19.3380 < 2.2e-16 ***      
                idOklahoma                     0.5502913   0.0976222   5.6369 2.307e-08 ***      
                idOregon                       1.4236463   0.1072424  13.2750 < 2.2e-16 ***      
                idPennsylvania                 2.3660500   0.1199959  19.7178 < 2.2e-16 ***      
                idRhodeIsland                  1.1345451   0.1923538   5.8982 5.171e-09 ***      
                idSouthCarolina                1.1438466   0.1390617   8.2255 6.654e-16 ***      
                idSouthDakota                 -0.5409167   0.1358824  -3.9808 7.415e-05 ***      
                idTennessee                    0.8876437   0.1006149   8.8222 < 2.2e-16 ***      
                idTexas                        2.5064488   0.1223233  20.4904 < 2.2e-16 ***      
                idUtah                         0.7645975   0.0990958   7.7157 3.146e-14 ***      
                idVermont                     -0.0054305   0.0965073  -0.0563 0.9551389          
                idVirginia                     1.6673294   0.1090390  15.2911 < 2.2e-16 ***      
                idWashington                   1.8852291   0.1114953  16.9086 < 2.2e-16 ***      
                idWestVirginia                -0.5391754   0.0980373  -5.4997 4.940e-08 ***      
                idWisconsin                    1.6728844   0.1082008  15.4609 < 2.2e-16 ***      
                idWyoming                     -0.2520479   0.1027182  -2.4538 0.0143222 *        
                time2001                      -2.3509494   0.4778964  -4.9194 1.030e-06 ***      
                time2002                      -2.2738431   0.4427120  -5.1362 3.428e-07 ***      
                time2003                      -2.2273932   0.3847175  -5.7897 9.693e-09 ***      
                time2004                      -2.3457877   0.2740976  -8.5582 < 2.2e-16 ***      
                time2005                      -2.0881419   0.2106976  -9.9106 < 2.2e-16 ***      
                time2006                      -1.5246372   0.1692602  -9.0077 < 2.2e-16 ***      
                time2007                      -1.0668421   0.1468762  -7.2635 8.078e-13 ***      
                time2008                      -0.7417974   0.1817142  -4.0822 4.852e-05 ***      
                time2009                      -0.0889422   0.2145442  -0.4146 0.6785589          
                time2010                      -0.0536982   0.1926270  -0.2788 0.7804861          
                time2011                       0.0484313   0.1401105   0.3457 0.7296743          
                time2012                       0.1694147   0.1274143   1.3296 0.1839701          
                time2013                      -0.0517685   0.1716581  -0.3016 0.7630417          
                time2014                      -0.2013221   0.2091030  -0.9628 0.3359082          
                time2015                       0.1101253   0.1002264   1.0988 0.2721600          
                time2016                       0.0468470   0.0911468   0.5140 0.6073954          
                iis75                         -1.1018357   0.3233891  -3.4072 0.0006851 ***      
                iis79                         -1.1945972   0.3239976  -3.6871 0.0002402 ***      
                iis164                        -1.0034540   0.3330403  -3.0130 0.0026581 **       
                iis235                        -0.9994070   0.3270031  -3.0563 0.0023064 **       
                iis236                         1.0796831   0.3280770   3.2909 0.0010368 **       
                iis237                        -0.8910575   0.3284684  -2.7128 0.0067980 **       
                iis238                        -1.0805123   0.3278157  -3.2961 0.0010182 **       
                iis346                        -1.0882917   0.3163121  -3.4406 0.0006068 ***      
                iis501                        -1.0199667   0.3164537  -3.2231 0.0013130 **       
                iis548                        -0.8616768   0.3246750  -2.6540 0.0080935 **       
                iis687                        -0.9487554   0.3173544  -2.9896 0.0028686 **       
                iis742                         1.1691074   0.3163359   3.6958 0.0002323 ***      
                iis829                         0.8692623   0.3219698   2.6998 0.0070659 **       
                iis839                        -1.2304399   0.3221306  -3.8197 0.0001427 ***      
                iis843                        -0.9689278   0.3163398  -3.0629 0.0022561 **       
                iis921                        -0.9847208   0.3165578  -3.1107 0.0019243 **       
                fesisAlaska.2007              -0.9936783   0.1732300  -5.7362 1.316e-08 ***      
                fesisAlaska.2014               0.6697021   0.1651291   4.0556 5.427e-05 ***      
                fesisArkansas.2002            -1.1838989   0.3447750  -3.4338 0.0006219 ***      
                fesisArkansas.2006            -0.7004627   0.2356400  -2.9726 0.0030305 **       
                fesisArkansas.2009             1.1341634   0.2032342   5.5806 3.160e-08 ***      
                fesisConnecticut.2009         -0.5741430   0.1417775  -4.0496 5.566e-05 ***      
                fesisDelaware.2014            -0.8734564   0.1459138  -5.9861 3.086e-09 ***      
                fesisDistrictofColumbia.2008  -0.8314279   0.1995239  -4.1671 3.379e-05 ***      
                fesisDistrictofColumbia.2012   1.0482009   0.1871571   5.6006 2.826e-08 ***      
                fesisHawaii.2009              -0.4996759   0.1547244  -3.2295 0.0012845 **       
                fesisMississippi.2004         -1.3722089   0.1961342  -6.9963 5.083e-12 ***      
                fesisMississippi.2020          1.3141438   0.3178669   4.1343 3.889e-05 ***      
                fesisNebraska.2012             0.5777925   0.1430648   4.0387 5.827e-05 ***      
                fesisNevada.2012              -0.5760822   0.1498992  -3.8431 0.0001299 ***      
                fesisNevada.2019               0.9001138   0.2472292   3.6408 0.0002871 ***      
                fesisRhodeIsland.2004         -0.8194007   0.1938512  -4.2270 2.607e-05 ***      
                fesisSouthCarolina.2008        0.7655921   0.1464035   5.2293 2.110e-07 ***      
                fesisSouthDakota.2008          0.6115876   0.1502517   4.0704 5.099e-05 ***      
                fesisWyoming.2017             -0.7676446   0.1953669  -3.9292 9.164e-05 ***      
                fesisWyoming.2020              1.5977885   0.3561357   4.4865 8.165e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                     Chi-sq df p-value      
                Ljung-Box AR(1)   0.4264963  1  0.5137      
                Ljung-Box ARCH(1) 0.0013378  1  0.9708      
                                                 
                SE of regression    0.30518      
                R-squared           0.94634      
                Log-lik.(n=1020) -183.21348      
us_q25

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 13:59:59 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                                   coef  std.error   t-stat   p-value          
                ar1                            0.048150   0.030664   1.5703 0.1167678          
                lgdp                          50.381818   2.996471  16.8137 < 2.2e-16 ***      
                lpop                         -38.542994   1.815101 -21.2346 < 2.2e-16 ***      
                lgdp_sq                       -1.874005   0.179764 -10.4248 < 2.2e-16 ***      
                avg_temp                      -0.109261   0.072409  -1.5089 0.1317241          
                idArizona                      1.597192   0.101880  15.6772 < 2.2e-16 ***      
                idCalifornia                   3.749866   0.149729  25.0444 < 2.2e-16 ***      
                idColorado                     1.921050   0.107137  17.9307 < 2.2e-16 ***      
                idConnecticut                  2.536803   0.141661  17.9075 < 2.2e-16 ***      
                idDelaware                     1.468022   0.109258  13.4363 < 2.2e-16 ***      
                idDistrictofColumbia           0.210729   0.128230   1.6434 0.1007184          
                idFlorida                      2.006081   0.108623  18.4682 < 2.2e-16 ***      
                idGeorgia                      1.369739   0.098605  13.8912 < 2.2e-16 ***      
                idHawaii                       0.318694   0.115369   2.7624 0.0058755 **       
                idIdaho                        0.213042   0.087449   2.4362 0.0150696 *        
                idIllinois                     2.019727   0.109374  18.4662 < 2.2e-16 ***      
                idIndiana                      0.961687   0.092647  10.3802 < 2.2e-16 ***      
                idIowa                         0.155357   0.088602   1.7534 0.0799299 .        
                idKansas                      -0.076993   0.088271  -0.8722 0.3833524          
                idKentucky                     0.127760   0.088358   1.4459 0.1486045          
                idLouisiana                    0.168785   0.106967   1.5779 0.1149974          
                idMaine                        0.190311   0.089540   2.1254 0.0338693 *        
                idMaryland                     1.259557   0.096264  13.0844 < 2.2e-16 ***      
                idMassachusetts                2.659289   0.122974  21.6248 < 2.2e-16 ***      
                idMichigan                     2.220761   0.113572  19.5538 < 2.2e-16 ***      
                idMinnesota                    1.820142   0.105854  17.1949 < 2.2e-16 ***      
                idMissouri                     0.728479   0.090975   8.0075 4.345e-15 ***      
                idNevada                       0.869089   0.107826   8.0601 2.924e-15 ***      
                idNewHampshire                 0.846775   0.092018   9.2023 < 2.2e-16 ***      
                idNewJersey                    1.903093   0.107175  17.7570 < 2.2e-16 ***      
                idNewMexico                    0.965227   0.092924  10.3873 < 2.2e-16 ***      
                idNewYork                      2.871926   0.128295  22.3853 < 2.2e-16 ***      
                idNorthCarolina                1.912798   0.107174  17.8476 < 2.2e-16 ***      
                idOhio                         2.224872   0.114121  19.4957 < 2.2e-16 ***      
                idOklahoma                     0.496638   0.088561   5.6079 2.861e-08 ***      
                idOregon                       2.035442   0.181539  11.2122 < 2.2e-16 ***      
                idPennsylvania                 2.285074   0.115030  19.8650 < 2.2e-16 ***      
                idRhodeIsland                  1.094254   0.173082   6.3222 4.378e-10 ***      
                idSouthCarolina                1.099353   0.126571   8.6856 < 2.2e-16 ***      
                idSouthDakota                 -0.747299   0.129321  -5.7786 1.096e-08 ***      
                idTennessee                    0.828207   0.091794   9.0224 < 2.2e-16 ***      
                idTexas                        2.423613   0.117702  20.5911 < 2.2e-16 ***      
                idUtah                         0.707186   0.090376   7.8249 1.687e-14 ***      
                idVermont                     -0.051661   0.087132  -0.5929 0.5534218          
                idVirginia                     1.595756   0.101864  15.6656 < 2.2e-16 ***      
                idWashington                   1.811725   0.105169  17.2267 < 2.2e-16 ***      
                idWisconsin                    1.602716   0.101296  15.8221 < 2.2e-16 ***      
                time2001                      -2.997513   0.469395  -6.3859 2.953e-10 ***      
                time2002                      -2.838060   0.435738  -6.5132 1.331e-10 ***      
                time2003                      -2.815543   0.376819  -7.4719 2.161e-13 ***      
                time2004                      -2.815199   0.268750 -10.4752 < 2.2e-16 ***      
                time2005                      -2.479312   0.205686 -12.0539 < 2.2e-16 ***      
                time2006                      -1.875591   0.166120 -11.2906 < 2.2e-16 ***      
                time2007                      -1.369228   0.144218  -9.4942 < 2.2e-16 ***      
                time2008                      -1.045792   0.175990  -5.9423 4.264e-09 ***      
                time2009                      -0.354983   0.208458  -1.7029 0.0889925 .        
                time2010                      -0.268915   0.186562  -1.4414 0.1498746          
                time2011                      -0.140947   0.136929  -1.0293 0.3036440          
                time2012                       0.069034   0.126311   0.5465 0.5848530          
                time2013                      -0.189504   0.165645  -1.1440 0.2529638          
                time2014                      -0.390724   0.201671  -1.9374 0.0530601 .        
                time2015                       0.032707   0.098461   0.3322 0.7398418          
                time2016                       0.018261   0.090175   0.2025 0.8395789          
                iis17                         -0.930854   0.282595  -3.2940 0.0010333 **       
                iis124                        -1.027710   0.297476  -3.4548 0.0005811 ***      
                iis195                        -1.014854   0.291837  -3.4775 0.0005347 ***      
                iis196                         1.074181   0.293242   3.6631 0.0002663 ***      
                iis197                        -0.942726   0.293946  -3.2071 0.0013963 **       
                iis198                        -1.096705   0.292896  -3.7443 0.0001944 ***      
                iis262                         0.912398   0.282833   3.2259 0.0013090 **       
                iis306                        -1.045654   0.282334  -3.7036 0.0002278 ***      
                iis344                        -1.031485   0.282994  -3.6449 0.0002856 ***      
                iis350                        -0.979129   0.282926  -3.4607 0.0005685 ***      
                iis441                        -0.985085   0.282460  -3.4875 0.0005153 ***      
                iis704                         1.307053   0.297343   4.3958 1.260e-05 ***      
                iis714                         0.799416   0.291828   2.7393 0.0062994 **       
                iis717                         0.908078   0.292103   3.1088 0.0019483 **       
                iis723                        -0.938517   0.282374  -3.3237 0.0009307 ***      
                iis801                        -0.945908   0.282533  -3.3480 0.0008539 ***      
                fesisConnecticut.2009         -0.597462   0.127036  -4.7031 3.039e-06 ***      
                fesisDelaware.2014            -0.868247   0.130801  -6.6379 6.022e-11 ***      
                fesisDistrictofColumbia.2008  -1.038788   0.195144  -5.3232 1.341e-07 ***      
                fesisDistrictofColumbia.2011   1.168696   0.182643   6.3988 2.726e-10 ***      
                fesisHawaii.2009              -0.516934   0.138393  -3.7353 0.0002014 ***      
                fesisKansas.2020               1.062604   0.282395   3.7628 0.0001808 ***      
                fesisLouisiana.2011           -0.700357   0.164303  -4.2626 2.273e-05 ***      
                fesisLouisiana.2015            0.860934   0.178887   4.8127 1.794e-06 ***      
                fesisNevada.2012              -0.607927   0.134177  -4.5308 6.814e-06 ***      
                fesisNevada.2019               0.986200   0.220642   4.4697 9.017e-06 ***      
                fesisOregon.2004              -0.730791   0.173500  -4.2120 2.832e-05 ***      
                fesisRhodeIsland.2004         -0.834461   0.173413  -4.8120 1.800e-06 ***      
                fesisSouthCarolina.2008        0.726480   0.131002   5.5456 4.035e-08 ***      
                fesisSouthDakota.2008          1.289298   0.195636   6.5903 8.165e-11 ***      
                fesisSouthDakota.2011         -0.892708   0.186407  -4.7890 2.012e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                     Chi-sq df p-value      
                Ljung-Box AR(1)   0.4876712  1  0.4850      
                Ljung-Box ARCH(1) 0.0056268  1  0.9402      
                                                
                SE of regression   0.27189      
                R-squared          0.94729      
                Log-lik.(n=860)  -53.25992      

0.05

us_all

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 13:55:37 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                                    coef   std.error   t-stat   p-value          
                ar1                            0.0142064   0.0275714   0.5153 0.6065031          
                lgdp                          45.4762662   2.8330892  16.0518 < 2.2e-16 ***      
                lpop                         -34.8991182   1.7332293 -20.1353 < 2.2e-16 ***      
                lgdp_sq                       -1.6765453   0.1689815  -9.9215 < 2.2e-16 ***      
                avg_temp                      -0.1171333   0.0680490  -1.7213 0.0855488 .        
                idAlaska                      -0.6360663   0.1406455  -4.5225 6.956e-06 ***      
                idArizona                      1.6926609   0.1027904  16.4671 < 2.2e-16 ***      
                idArkansas                     0.7319626   0.2828212   2.5881 0.0098118 **       
                idCalifornia                   3.9216787   0.1425169  27.5173 < 2.2e-16 ***      
                idColorado                     2.0270836   0.1070324  18.9390 < 2.2e-16 ***      
                idConnecticut                  2.6561453   0.1391969  19.0819 < 2.2e-16 ***      
                idDelaware                     1.5572386   0.1102846  14.1202 < 2.2e-16 ***      
                idDistrictofColumbia           0.2371182   0.1305958   1.8157 0.0697647 .        
                idFlorida                      2.1149043   0.1082385  19.5393 < 2.2e-16 ***      
                idGeorgia                      1.4578627   0.1001693  14.5540 < 2.2e-16 ***      
                idHawaii                       0.3528882   0.1180609   2.9890 0.0028771 **       
                idIdaho                       -0.5205351   0.2824725  -1.8428 0.0656998 .        
                idIllinois                     2.1299347   0.1088493  19.5677 < 2.2e-16 ***      
                idIndiana                      1.0335661   0.0954468  10.8287 < 2.2e-16 ***      
                idIowa                        -0.3374395   0.2824575  -1.1947 0.2325461          
                idKansas                       0.0071362   0.0933441   0.0765 0.9390784          
                idKentucky                     0.1700069   0.0922854   1.8422 0.0657870 .        
                idLouisiana                    0.2141295   0.1098983   1.9484 0.0516832 .        
                idMaine                        0.2266892   0.0934303   2.4263 0.0154556 *        
                idMaryland                     1.3418822   0.0983065  13.6500 < 2.2e-16 ***      
                idMassachusetts                2.7923749   0.1200267  23.2646 < 2.2e-16 ***      
                idMichigan                     2.3384225   0.1122758  20.8275 < 2.2e-16 ***      
                idMinnesota                    1.9237041   0.1059931  18.1493 < 2.2e-16 ***      
                idMississippi                  0.4714723   0.1721045   2.7395 0.0062796 **       
                idMissouri                     0.7924166   0.0943493   8.3988 < 2.2e-16 ***      
                idMontana                     -0.4101271   0.0931977  -4.4006 1.213e-05 ***      
                idNebraska                    -0.3197774   0.1191021  -2.6849 0.0073927 **       
                idNevada                       0.9370904   0.1099992   8.5191 < 2.2e-16 ***      
                idNewHampshire                 0.9165509   0.0949521   9.6528 < 2.2e-16 ***      
                idNewJersey                    2.0091974   0.1070626  18.7666 < 2.2e-16 ***      
                idNewMexico                    1.0379993   0.0956652  10.8503 < 2.2e-16 ***      
                idNewYork                      3.0131910   0.1244533  24.2114 < 2.2e-16 ***      
                idNorthCarolina                2.0189019   0.1070623  18.8573 < 2.2e-16 ***      
                idNorthDakota                 -0.5933094   0.1406959  -4.2170 2.734e-05 ***      
                idOhio                         2.3434788   0.1127260  20.7892 < 2.2e-16 ***      
                idOklahoma                     0.5512035   0.0922432   5.9755 3.337e-09 ***      
                idOregon                       1.8756612   0.2142395   8.7550 < 2.2e-16 ***      
                idPennsylvania                 2.4052302   0.1134717  21.1967 < 2.2e-16 ***      
                idRhodeIsland                  1.1527243   0.1740107   6.6244 6.090e-11 ***      
                idSouthCarolina                1.1707384   0.1279074   9.1530 < 2.2e-16 ***      
                idSouthDakota                 -0.7389781   0.1314938  -5.6199 2.571e-08 ***      
                idTennessee                    0.8937178   0.0949772   9.4098 < 2.2e-16 ***      
                idTexas                        2.5482327   0.1156686  22.0305 < 2.2e-16 ***      
                idUtah                         0.7707740   0.0936632   8.2292 6.820e-16 ***      
                idVermont                     -0.0280691   0.1134343  -0.2474 0.8046200          
                idVirginia                     1.6916023   0.1029898  16.4249 < 2.2e-16 ***      
                idWashington                   1.9139437   0.1054398  18.1520 < 2.2e-16 ***      
                idWestVirginia                -0.3913969   0.1043218  -3.7518 0.0001871 ***      
                idWisconsin                    1.6969272   0.1023218  16.5842 < 2.2e-16 ***      
                idWyoming                     -0.2667085   0.0961038  -2.7752 0.0056345 **       
                time2001                      -2.6685160   0.4403128  -6.0605 2.017e-09 ***      
                time2002                      -2.5829034   0.4085195  -6.3226 4.100e-10 ***      
                time2003                      -2.5377536   0.3537105  -7.1747 1.548e-12 ***      
                time2004                      -2.5676566   0.2523099 -10.1766 < 2.2e-16 ***      
                time2005                      -2.2597329   0.1934234 -11.6828 < 2.2e-16 ***      
                time2006                      -1.6534965   0.1563605 -10.5749 < 2.2e-16 ***      
                time2007                      -1.1657045   0.1356445  -8.5938 < 2.2e-16 ***      
                time2008                      -0.8881006   0.1655882  -5.3633 1.047e-07 ***      
                time2009                      -0.2836173   0.1957586  -1.4488 0.1477493          
                time2010                      -0.2149167   0.1754113  -1.2252 0.2208245          
                time2011                      -0.0243147   0.1286032  -0.1891 0.8500836          
                time2012                       0.1381183   0.1178826   1.1717 0.2416535          
                time2013                      -0.1365243   0.1560648  -0.8748 0.3819275          
                time2014                      -0.3575761   0.1898236  -1.8837 0.0599339 .        
                time2015                       0.0639017   0.0918337   0.6958 0.4867135          
                time2016                       0.0440108   0.0837785   0.5253 0.5994917          
                iis19                          0.8429755   0.3358763   2.5098 0.0122606 *        
                iis23                          0.6547980   0.3004510   2.1794 0.0295698 *        
                iis66                         -1.3545132   0.2898907  -4.6725 3.445e-06 ***      
                iis67                         -1.1056380   0.2900202  -3.8123 0.0001474 ***      
                iis68                         -1.1241548   0.2894683  -3.8835 0.0001107 ***      
                iis75                         -1.1705698   0.2890080  -4.0503 5.570e-05 ***      
                iis77                         -0.7611034   0.2894520  -2.6295 0.0087024 **       
                iis79                         -1.2093311   0.2897269  -4.1740 3.292e-05 ***      
                iis164                        -0.9945085   0.2962174  -3.3574 0.0008209 ***      
                iis168                        -0.8367098   0.3187966  -2.6246 0.0088270 **       
                iis235                        -1.0009331   0.2907491  -3.4426 0.0006035 ***      
                iis236                         1.0602884   0.2918464   3.6330 0.0002965 ***      
                iis237                        -0.8746018   0.2924569  -2.9905 0.0028631 **       
                iis238                        -1.1070224   0.2917033  -3.7950 0.0001578 ***      
                iis331                        -0.8221422   0.2816705  -2.9188 0.0036040 **       
                iis346                        -1.0669132   0.2813273  -3.7924 0.0001595 ***      
                iis379                         0.6860894   0.3003414   2.2844 0.0225893 *        
                iis384                        -1.0256127   0.2818531  -3.6388 0.0002900 ***      
                iis390                        -0.9295938   0.2818830  -3.2978 0.0010138 **       
                iis493                        -0.5739980   0.2889381  -1.9866 0.0472815 *        
                iis501                        -1.0340557   0.2815395  -3.6729 0.0002544 ***      
                iis532                        -0.6360743   0.2820027  -2.2556 0.0243450 *        
                iis543                        -0.5792785   0.2908451  -1.9917 0.0467143 *        
                iis548                        -0.9970587   0.2921446  -3.4129 0.0006723 ***      
                iis550                        -0.8392576   0.2908544  -2.8855 0.0040043 **       
                iis578                        -0.6215469   0.2962834  -2.0978 0.0362087 *        
                iis687                        -0.8675048   0.2875018  -3.0174 0.0026236 **       
                iis691                        -0.7893330   0.2863381  -2.7566 0.0059615 **       
                iis742                         0.7632657   0.3362041   2.2702 0.0234357 *        
                iis817                         0.6745806   0.2865013   2.3545 0.0187659 *        
                iis818                         0.6399595   0.2869796   2.2300 0.0260022 *        
                iis824                         1.3312169   0.2961178   4.4956 7.874e-06 ***      
                iis829                         1.0748760   0.2960428   3.6308 0.0002990 ***      
                iis830                         0.8802536   0.2972176   2.9616 0.0031429 **       
                iis834                         0.6149207   0.2960124   2.0773 0.0380613 *        
                iis837                         0.7400137   0.2964074   2.4966 0.0127220 *        
                iis843                        -0.9527531   0.2813988  -3.3858 0.0007415 ***      
                iis921                        -1.0043151   0.2816251  -3.5661 0.0003820 ***      
                iis973                        -0.6451421   0.2939433  -2.1948 0.0284418 *        
                fesisAlabama.2017             -0.8542641   0.2828996  -3.0197 0.0026041 **       
                fesisAlabama.2018              0.7977194   0.3360400   2.3739 0.0178176 *        
                fesisAlaska.2007              -0.9224536   0.1624429  -5.6786 1.849e-08 ***      
                fesisAlaska.2014               0.6842213   0.1469388   4.6565 3.716e-06 ***      
                fesisArkansas.2002            -1.1503231   0.3066590  -3.7511 0.0001876 ***      
                fesisArkansas.2006             0.4820965   0.1650200   2.9214 0.0035739 **       
                fesisConnecticut.2009         -0.6019968   0.1263936  -4.7629 2.234e-06 ***      
                fesisDelaware.2014            -0.7732195   0.1367660  -5.6536 2.128e-08 ***      
                fesisDelaware.2020            -0.8043484   0.2963005  -2.7146 0.0067658 **       
                fesisDistrictofColumbia.2008  -0.6476123   0.1952276  -3.3172 0.0009468 ***      
                fesisDistrictofColumbia.2012   0.8531177   0.1858937   4.5893 5.100e-06 ***      
                fesisHawaii.2009              -0.5230715   0.1378057  -3.7957 0.0001574 ***      
                fesisIdaho.2002                0.8198288   0.2815590   2.9117 0.0036856 **       
                fesisIowa.2002                 1.4589331   0.3879040   3.7611 0.0001805 ***      
                fesisIowa.2003                -0.8921974   0.2822084  -3.1615 0.0016238 **       
                fesisKansas.2020               0.9275503   0.2819530   3.2897 0.0010430 **       
                fesisLouisiana.2011           -0.7243172   0.1634276  -4.4320 1.052e-05 ***      
                fesisLouisiana.2015            0.7719463   0.1849459   4.1739 3.294e-05 ***      
                fesisMississippi.2004         -1.1676822   0.1947663  -5.9953 2.970e-09 ***      
                fesisMississippi.2010         -0.3180443   0.1454499  -2.1866 0.0290347 *        
                fesisMississippi.2020          1.4003182   0.2891629   4.8427 1.515e-06 ***      
                fesisNebraska.2012             0.4327658   0.1345522   3.2163 0.0013461 **       
                fesisNevada.2012              -0.5195463   0.1402185  -3.7053 0.0002245 ***      
                fesisNevada.2019               0.8465380   0.2239613   3.7798 0.0001676 ***      
                fesisNorthDakota.2006          0.7979092   0.3005943   2.6544 0.0080886 **       
                fesisNorthDakota.2007         -0.8054294   0.2865599  -2.8107 0.0050543 **       
                fesisNorthDakota.2020          0.8756288   0.2865472   3.0558 0.0023129 **       
                fesisOregon.2004              -0.4834731   0.2063511  -2.3430 0.0193549 *        
                fesisRhodeIsland.2004         -0.8406381   0.1726012  -4.8704 1.322e-06 ***      
                fesisSouthCarolina.2008        0.6595474   0.1341240   4.9174 1.048e-06 ***      
                fesisSouthDakota.2008          0.6130910   0.1593013   3.8486 0.0001274 ***      
                fesisSouthDakota.2018         -0.4428768   0.1941681  -2.2809 0.0227949 *        
                fesisVermont.2010              0.5556208   0.1830882   3.0347 0.0024790 **       
                fesisVermont.2013             -0.7310920   0.1860829  -3.9289 9.209e-05 ***      
                fesisWestVirginia.2013        -0.3406067   0.1316382  -2.5874 0.0098296 **       
                fesisWyoming.2017             -0.7785183   0.1740541  -4.4729 8.737e-06 ***      
                fesisWyoming.2020              1.6053993   0.3168407   5.0669 4.936e-07 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                     Chi-sq df p-value      
                Ljung-Box AR(1)   0.0015689  1  0.9684      
                Ljung-Box ARCH(1) 0.1172142  1  0.7321      
                                                
                SE of regression   0.27130      
                R-squared          0.95945      
                Log-lik.(n=1020) -43.20138      
us_q25

                Formula: log_patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 13:59:55 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                                    coef   std.error   t-stat   p-value          
                ar1                            0.0349214   0.0287736   1.2137 0.2252642          
                lgdp                          47.5066364   2.7642437  17.1861 < 2.2e-16 ***      
                lpop                         -37.7705401   1.6736542 -22.5677 < 2.2e-16 ***      
                lgdp_sq                       -1.7071350   0.1656425 -10.3061 < 2.2e-16 ***      
                avg_temp                      -0.0491806   0.0677436  -0.7260 0.4680797          
                idArizona                      1.4082364   0.1005593  14.0040 < 2.2e-16 ***      
                idCalifornia                   3.5906635   0.1451917  24.7305 < 2.2e-16 ***      
                idColorado                     1.7362117   0.1055019  16.4567 < 2.2e-16 ***      
                idConnecticut                  2.3583386   0.1359096  17.3523 < 2.2e-16 ***      
                idDelaware                     1.2792769   0.1065460  12.0068 < 2.2e-16 ***      
                idDistrictofColumbia          -0.0043637   0.1208177  -0.0361 0.9711978          
                idFlorida                      1.8223297   0.1068944  17.0479 < 2.2e-16 ***      
                idGeorgia                      1.1779204   0.0974610  12.0861 < 2.2e-16 ***      
                idHawaii                       0.3174875   0.1413539   2.2460 0.0249953 *        
                idIdaho                       -0.7320769   0.2574897  -2.8431 0.0045904 **       
                idIllinois                     1.8365156   0.1075976  17.0684 < 2.2e-16 ***      
                idIndiana                      0.7635373   0.0917443   8.3224 4.144e-16 ***      
                idIowa                        -0.5478526   0.2574475  -2.1280 0.0336656 *        
                idKansas                      -0.1752352   0.0902118  -1.9425 0.0524573 .        
                idKentucky                    -0.0808486   0.0870484  -0.9288 0.3533076          
                idLouisiana                   -0.0387634   0.1028769  -0.3768 0.7064346          
                idMaine                       -0.0212876   0.0878377  -0.2424 0.8085754          
                idMaryland                     1.0654785   0.0952315  11.1883 < 2.2e-16 ***      
                idMassachusetts                2.4849939   0.1202905  20.6583 < 2.2e-16 ***      
                idMichigan                     2.0404541   0.1115218  18.2965 < 2.2e-16 ***      
                idMinnesota                    1.6343403   0.1042979  15.6699 < 2.2e-16 ***      
                idMissouri                     0.5266584   0.0899238   5.8567 7.099e-09 ***      
                idNevada                       0.6716411   0.1044465   6.4305 2.281e-10 ***      
                idNewHampshire                 0.6478060   0.0911299   7.1086 2.765e-12 ***      
                idNewJersey                    1.7182823   0.1055369  16.2813 < 2.2e-16 ***      
                idNewMexico                    0.7674255   0.0920142   8.3403 3.611e-16 ***      
                idNewYork                      3.0957505   0.1731312  17.8809 < 2.2e-16 ***      
                idNorthCarolina                1.7279873   0.1055365  16.3734 < 2.2e-16 ***      
                idOhio                         2.0449339   0.1120349  18.2527 < 2.2e-16 ***      
                idOklahoma                     0.2917411   0.0876451   3.3287 0.0009158 ***      
                idOregon                       1.6183498   0.1994162   8.1154 2.015e-15 ***      
                idPennsylvania                 2.1057394   0.1128837  18.6541 < 2.2e-16 ***      
                idRhodeIsland                  0.8958738   0.1610529   5.5626 3.715e-08 ***      
                idSouthCarolina                0.9020965   0.1207260   7.4723 2.228e-13 ***      
                idSouthDakota                 -0.8690422   0.1297695  -6.6968 4.214e-11 ***      
                idTennessee                    0.6261176   0.0907423   6.9000 1.118e-11 ***      
                idTexas                        2.2460183   0.1153765  19.4669 < 2.2e-16 ***      
                idUtah                         0.5503750   0.0903776   6.0897 1.817e-09 ***      
                idVermont                     -0.1930644   0.1095292  -1.7627 0.0783679 .        
                idVirginia                     1.4063711   0.1004399  14.0021 < 2.2e-16 ***      
                idWashington                   1.6253998   0.1036552  15.6808 < 2.2e-16 ***      
                idWisconsin                    1.4132700   0.1000082  14.1315 < 2.2e-16 ***      
                time2001                      -2.5325059   0.4328311  -5.8510 7.336e-09 ***      
                time2002                      -2.4301519   0.4015891  -6.0513 2.281e-09 ***      
                time2003                      -2.4246151   0.3477952  -6.9714 6.958e-12 ***      
                time2004                      -2.5260542   0.2480841 -10.1822 < 2.2e-16 ***      
                time2005                      -2.2476711   0.1901655 -11.8195 < 2.2e-16 ***      
                time2006                      -1.6868433   0.1531524 -11.0141 < 2.2e-16 ***      
                time2007                      -1.2399096   0.1325860  -9.3517 < 2.2e-16 ***      
                time2008                      -0.8081995   0.1638604  -4.9322 1.004e-06 ***      
                time2009                      -0.1121420   0.1932430  -0.5803 0.5618783          
                time2010                      -0.0233793   0.1737535  -0.1346 0.8930007          
                time2011                       0.0176574   0.1266905   0.1394 0.8891922          
                time2012                       0.1264023   0.1159518   1.0901 0.2760116          
                time2013                       0.0247746   0.1551251   0.1597 0.8731553          
                time2014                      -0.1326702   0.1887564  -0.7029 0.4823613          
                time2015                       0.1011938   0.0902419   1.1214 0.2624978          
                time2016                       0.0256526   0.0825972   0.3106 0.7562112          
                iis2                          -0.8854658   0.2578510  -3.4340 0.0006278 ***      
                iis4                          -0.8496240   0.2579189  -3.2942 0.0010342 **       
                iis10                         -1.0378375   0.2576745  -4.0277 6.214e-05 ***      
                iis13                         -0.7535883   0.2580373  -2.9205 0.0036014 **       
                iis17                         -1.1241135   0.2579215  -4.3584 1.496e-05 ***      
                iis124                        -1.0126709   0.2690411  -3.7640 0.0001805 ***      
                iis128                        -0.6769694   0.3076641  -2.2004 0.0280902 *        
                iis138                         0.5282001   0.2627541   2.0102 0.0447677 *        
                iis195                        -1.0005419   0.2638264  -3.7924 0.0001614 ***      
                iis196                         1.0752858   0.2652155   4.0544 5.559e-05 ***      
                iis197                        -0.9087822   0.2659456  -3.4172 0.0006673 ***      
                iis198                        -1.0809454   0.2650684  -4.0780 5.035e-05 ***      
                iis262                         0.8637161   0.2564243   3.3683 0.0007955 ***      
                iis282                        -0.6095332   0.2567820  -2.3737 0.0178634 *        
                iis286                        -0.6743274   0.2565735  -2.6282 0.0087617 **       
                iis291                        -0.8546658   0.2564196  -3.3331 0.0009016 ***      
                iis306                        -1.0757248   0.2553960  -4.2120 2.843e-05 ***      
                iis344                        -1.0266985   0.2559292  -4.0117 6.642e-05 ***      
                iis350                        -0.9700523   0.2559610  -3.7898 0.0001630 ***      
                iis441                        -0.9926507   0.2555706  -3.8841 0.0001119 ***      
                iis478                        -0.6151065   0.2689941  -2.2867 0.0224954 *        
                iis622                         0.6984264   0.3054322   2.2867 0.0224960 *        
                iis697                         0.6598034   0.2600207   2.5375 0.0113688 *        
                iis698                         0.6341506   0.2606811   2.4327 0.0152240 *        
                iis704                         1.2181777   0.2727095   4.4669 9.174e-06 ***      
                iis706                        -0.6023497   0.2726447  -2.2093 0.0274604 *        
                iis709                         1.0195445   0.2622529   3.8876 0.0001103 ***      
                iis710                         0.7859279   0.2639740   2.9773 0.0030030 **       
                iis717                         0.6867894   0.2624762   2.6166 0.0090628 **       
                iis719                        -1.1161850   0.2623762  -4.2541 2.368e-05 ***      
                iis723                        -0.9149032   0.2553118  -3.5835 0.0003613 ***      
                iis779                        -0.8913992   0.2553773  -3.4905 0.0005107 ***      
                iis782                        -0.7138460   0.2641560  -2.7024 0.0070426 **       
                iis801                        -0.9571515   0.2556327  -3.7442 0.0001950 ***      
                fesisAlabama.2020             -0.5112122   0.2587650  -1.9756 0.0485730 *        
                fesisConnecticut.2009         -0.6012081   0.1150525  -5.2255 2.261e-07 ***      
                fesisDelaware.2014            -0.8835584   0.1184771  -7.4576 2.471e-13 ***      
                fesisDistrictofColumbia.2008  -0.8093555   0.2050207  -3.9477 8.644e-05 ***      
                fesisDistrictofColumbia.2011   0.8928709   0.1979776   4.5100 7.538e-06 ***      
                fesisHawaii.2005              -0.6336003   0.1902849  -3.3297 0.0009123 ***      
                fesisHawaii.2008               0.8508617   0.2872940   2.9616 0.0031580 **       
                fesisHawaii.2009              -0.9525569   0.2641386  -3.6063 0.0003315 ***      
                fesisIdaho.2002                0.7753635   0.2555725   3.0338 0.0024992 **       
                fesisIowa.2002                 0.5230103   0.2559637   2.0433 0.0413766 *        
                fesisKansas.2020               0.9254180   0.2565929   3.6066 0.0003311 ***      
                fesisLouisiana.2011           -0.7074510   0.1487030  -4.7575 2.357e-06 ***      
                fesisLouisiana.2015            0.8639365   0.1618297   5.3386 1.247e-07 ***      
                fesisNevada.2012              -0.5191356   0.1275162  -4.0711 5.182e-05 ***      
                fesisNevada.2019               0.8515149   0.2032366   4.1898 3.129e-05 ***      
                fesisNewYork.2005             -0.4936650   0.1398930  -3.5289 0.0004431 ***      
                fesisOregon.2004              -0.5066273   0.1877314  -2.6987 0.0071202 **       
                fesisRhodeIsland.2004         -0.7837781   0.1584164  -4.9476 9.308e-07 ***      
                fesisRhodeIsland.2019         -0.5012195   0.1877715  -2.6693 0.0077674 **       
                fesisSouthCarolina.2008        0.6385987   0.1219460   5.2367 2.132e-07 ***      
                fesisSouthDakota.2008          0.5386327   0.1397387   3.8546 0.0001260 ***      
                fesisVermont.2010              0.4699610   0.1687406   2.7851 0.0054878 **       
                fesisVermont.2013             -0.7330607   0.1689421  -4.3391 1.629e-05 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                    Chi-sq df p-value      
                Ljung-Box AR(1)   0.011377  1  0.9151      
                Ljung-Box ARCH(1) 0.165674  1  0.6840      
                                               
                SE of regression  0.24578      
                R-squared         0.95839      
                Log-lik.(n=860)  46.56933      

Patent Count

0.01

us_all

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 13:46:32 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                            coef   std.error  t-stat   p-value          
                ar1                   6.0292e-01  2.4855e-02 24.2579 < 2.2e-16 ***      
                lgdp                  4.3358e+02  5.5343e+01  7.8344 1.297e-14 ***      
                lpop                 -3.1823e+02  3.4082e+01 -9.3369 < 2.2e-16 ***      
                lgdp_sq              -1.7238e+01  3.3042e+00 -5.2169 2.249e-07 ***      
                avg_temp             -3.0570e-01  1.3549e+00 -0.2256 0.8215440          
                idAlaska             -1.0850e+00  1.7630e+00 -0.6154 0.5384368          
                idArizona             6.8648e+00  1.8160e+00  3.7802 0.0001668 ***      
                idArkansas           -3.3404e-01  1.7617e+00 -0.1896 0.8496508          
                idCalifornia         -5.6185e+01  7.2052e+00 -7.7978 1.704e-14 ***      
                idColorado            1.0741e+01  1.8846e+00  5.6996 1.617e-08 ***      
                idConnecticut         1.3403e+01  1.9701e+00  6.8033 1.842e-11 ***      
                idDelaware            4.1195e+00  1.7830e+00  2.3104 0.0210842 *        
                idDistrictofColumbia  2.3088e-01  1.7615e+00  0.1311 0.8957494          
                idFlorida             1.1375e+01  1.8974e+00  5.9951 2.920e-09 ***      
                idGeorgia             3.5082e+00  1.8185e+00  1.9292 0.0540104 .        
                idHawaii             -5.5834e-02  1.7615e+00 -0.0317 0.9747208          
                idIdaho               4.2025e-01  1.7616e+00  0.2386 0.8115013          
                idIllinois            1.0966e+01  1.8991e+00  5.7742 1.057e-08 ***      
                idIndiana             2.6099e+00  1.7687e+00  1.4756 0.1403880          
                idIowa                3.6037e-01  1.7616e+00  0.2046 0.8379506          
                idKansas             -5.0278e-02  1.7615e+00 -0.0285 0.9772354          
                idKentucky            1.2799e-01  1.7615e+00  0.0727 0.9420939          
                idLouisiana           7.7636e-02  1.7615e+00  0.0441 0.9648544          
                idMaine               2.2282e-01  1.7615e+00  0.1265 0.8993673          
                idMaryland            4.1364e+00  1.7797e+00  2.3242 0.0203315 *        
                idMassachusetts       1.9592e+01  2.3668e+00  8.2779 4.389e-16 ***      
                idMichigan            1.6090e+01  2.0117e+00  7.9983 3.780e-15 ***      
                idMinnesota           8.7953e+00  1.8498e+00  4.7548 2.305e-06 ***      
                idMississippi        -7.8571e-01  1.7624e+00 -0.4458 0.6558328          
                idMissouri            1.6491e+00  1.7641e+00  0.9348 0.3501551          
                idMontana            -6.2543e-01  1.7620e+00 -0.3550 0.7227019          
                idNebraska           -3.1543e-01  1.7617e+00 -0.1790 0.8579391          
                idNevada              1.5451e+00  1.7643e+00  0.8758 0.3813753          
                idNewHampshire        1.9167e+00  1.7671e+00  1.0847 0.2783524          
                idNewJersey           8.5328e+00  1.8933e+00  4.5069 7.428e-06 ***      
                idNewMexico           2.5894e+00  1.7693e+00  1.4635 0.1436776          
                idNewYork             3.4890e+01  2.8280e+00 12.3374 < 2.2e-16 ***      
                idNorthCarolina       9.9066e+00  1.8696e+00  5.2989 1.459e-07 ***      
                idNorthDakota        -7.5293e-01  1.7623e+00 -0.4272 0.6693092          
                idOhio                1.2795e+01  2.0175e+00  6.3419 3.554e-10 ***      
                idOklahoma            1.0447e+00  1.7624e+00  0.5928 0.5534690          
                idOregon              5.0704e+00  1.7914e+00  2.8305 0.0047494 **       
                idPennsylvania        1.3255e+01  2.0811e+00  6.3694 2.995e-10 ***      
                idRhodeIsland         6.8777e-01  1.7621e+00  0.3903 0.6963977          
                idSouthCarolina       7.6944e+00  1.8253e+00  4.2155 2.738e-05 ***      
                idSouthDakota         2.0902e-03  1.7615e+00  0.0012 0.9990535          
                idTennessee           2.1958e+00  1.7663e+00  1.2432 0.2141235          
                idTexas               1.7013e+01  2.1359e+00  7.9651 4.864e-15 ***      
                idUtah                1.9044e+00  1.7655e+00  1.0786 0.2810291          
                idVermont            -6.2903e-03  1.7615e+00 -0.0036 0.9971515          
                idVirginia            6.7309e+00  1.8109e+00  3.7169 0.0002139 ***      
                idWashington          8.9484e+00  1.8483e+00  4.8415 1.511e-06 ***      
                idWestVirginia       -7.1453e-01  1.7621e+00 -0.4055 0.6852098          
                idWisconsin           6.8605e+00  1.8106e+00  3.7890 0.0001611 ***      
                idWyoming            -5.5557e-01  1.7619e+00 -0.3153 0.7525838          
                time2001             -2.7119e+01  8.6322e+00 -3.1416 0.0017341 **       
                time2002             -2.5349e+01  8.0042e+00 -3.1670 0.0015909 **       
                time2003             -2.5283e+01  6.9398e+00 -3.6432 0.0002844 ***      
                time2004             -2.3571e+01  4.9415e+00 -4.7701 2.141e-06 ***      
                time2005             -2.0402e+01  3.7926e+00 -5.3795 9.480e-08 ***      
                time2006             -1.5350e+01  3.0567e+00 -5.0216 6.153e-07 ***      
                time2007             -1.1553e+01  2.6561e+00 -4.3494 1.518e-05 ***      
                time2008             -8.0488e+00  3.2803e+00 -2.4537 0.0143243 *        
                time2009             -2.8195e+00  3.8738e+00 -0.7278 0.4669081          
                time2010             -2.5196e+00  3.4790e+00 -0.7242 0.4691160          
                time2011             -3.1080e+00  2.5420e+00 -1.2227 0.2217753          
                time2012             -1.2883e+00  2.3251e+00 -0.5541 0.5796609          
                time2013             -2.0351e+00  3.1127e+00 -0.6538 0.5134095          
                time2014             -5.6511e+00  3.7855e+00 -1.4928 0.1358279          
                time2015             -4.2685e-01  1.8183e+00 -0.2347 0.8144573          
                time2016             -2.1486e+00  1.6631e+00 -1.2919 0.1967019          
                iis81                 1.0896e+02  8.3814e+00 13.0002 < 2.2e-16 ***      
                iis82                 8.6520e+01  8.2019e+00 10.5488 < 2.2e-16 ***      
                iis83                 9.2518e+01  8.2447e+00 11.2216 < 2.2e-16 ***      
                iis84                 1.2134e+02  8.2326e+00 14.7393 < 2.2e-16 ***      
                iis85                 1.2915e+02  8.0736e+00 15.9966 < 2.2e-16 ***      
                iis86                 2.0389e+02  7.9912e+00 25.5148 < 2.2e-16 ***      
                iis87                 1.7951e+02  8.0989e+00 22.1648 < 2.2e-16 ***      
                iis88                 2.0917e+02  8.2677e+00 25.2993 < 2.2e-16 ***      
                iis89                 2.1307e+02  8.6613e+00 24.5997 < 2.2e-16 ***      
                iis90                 1.6166e+02  9.0146e+00 17.9332 < 2.2e-16 ***      
                iis91                 1.7122e+02  8.6701e+00 19.7477 < 2.2e-16 ***      
                iis92                 1.6316e+02  8.5797e+00 19.0166 < 2.2e-16 ***      
                iis93                 1.6523e+02  8.4689e+00 19.5099 < 2.2e-16 ***      
                iis94                 1.1198e+02  8.4108e+00 13.3139 < 2.2e-16 ***      
                iis95                 1.4418e+02  8.0658e+00 17.8760 < 2.2e-16 ***      
                iis96                 1.4595e+02  8.0584e+00 18.1115 < 2.2e-16 ***      
                iis97                 1.1767e+02  8.0609e+00 14.5982 < 2.2e-16 ***      
                iis98                 1.3536e+02  7.9793e+00 16.9638 < 2.2e-16 ***      
                iis99                 1.1028e+02  7.9809e+00 13.8177 < 2.2e-16 ***      
                iis211                2.7836e+01  5.7771e+00  4.8183 1.693e-06 ***      
                iis426                2.8891e+01  5.7907e+00  4.9892 7.249e-07 ***      
                iis428                4.7837e+01  5.7811e+00  8.2747 4.499e-16 ***      
                iis453               -2.0389e+01  5.8091e+00 -3.5099 0.0004700 ***      
                iis613                2.5215e+01  5.7757e+00  4.3657 1.411e-05 ***      
                iis713                2.5637e+01  5.7787e+00  4.4364 1.026e-05 ***      
                iis767                3.2004e+01  5.7811e+00  5.5360 4.037e-08 ***      
                iis770                2.6024e+01  5.7841e+00  4.4992 7.694e-06 ***      
                iis869                2.8137e+01  5.7744e+00  4.8728 1.296e-06 ***      
                fesisNewYork.2012    -1.0138e+01  2.6148e+00 -3.8772 0.0001132 ***      
                fesisNewYork.2020    -3.2322e+01  5.9868e+00 -5.3989 8.537e-08 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df   p-value          
                Ljung-Box AR(1)    28.34  1 1.018e-07 ***      
                Ljung-Box ARCH(1)  19.89  1 8.205e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     5.57026      
                R-squared            0.97812      
                Log-lik.(n=1020) -3148.60778      
us_q25

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.01; AR: 1      
                      
                Date: Thu Mar 30 13:49:07 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                            coef   std.error  t-stat   p-value          
                ar1                     0.586819    0.028646 20.4855 < 2.2e-16 ***      
                lgdp                  512.651473   66.697683  7.6862 4.616e-14 ***      
                lpop                 -374.676937   41.096775 -9.1169 < 2.2e-16 ***      
                lgdp_sq               -20.506304    3.980691 -5.1514 3.286e-07 ***      
                avg_temp               -0.288779    1.632059 -0.1769 0.8596009          
                idArizona               7.150854    2.010086  3.5575 0.0003973 ***      
                idCalifornia          -51.609728    8.098333 -6.3729 3.190e-10 ***      
                idColorado             11.175507    2.092307  5.3412 1.216e-07 ***      
                idConnecticut          13.974502    2.194411  6.3682 3.284e-10 ***      
                idDelaware              4.298399    1.970466  2.1814 0.0294544 *        
                idDistrictofColumbia    0.237198    1.944623  0.1220 0.9029494          
                idFlorida              11.831951    2.107629  5.6139 2.761e-08 ***      
                idGeorgia               3.745095    2.011361  1.8620 0.0629875 .        
                idHawaii               -0.062659    1.944628 -0.0322 0.9743035          
                idIdaho                 0.434451    1.944754  0.2234 0.8232863          
                idIllinois             11.425339    2.109605  5.4159 8.155e-08 ***      
                idIndiana               2.713146    1.953249  1.3890 0.1652209          
                idIowa                  0.371601    1.944693  0.1911 0.8485095          
                idKansas               -0.056710    1.944624 -0.0292 0.9767427          
                idKentucky              0.132500    1.944607  0.0681 0.9456940          
                idLouisiana             0.079602    1.944593  0.0409 0.9673584          
                idMaine                 0.225873    1.944598  0.1162 0.9075606          
                idMaryland              4.301025    1.966521  2.1871 0.0290332 *        
                idMassachusetts        20.619574    2.661123  7.7484 2.934e-14 ***      
                idMichigan             16.730869    2.242694  7.4602 2.333e-13 ***      
                idMinnesota             9.161096    2.050601  4.4675 9.098e-06 ***      
                idMissouri              1.711975    1.947809  0.8789 0.3797167          
                idNevada                1.609301    1.947941  0.8262 0.4089716          
                idNewHampshire          2.007639    1.951313  1.0289 0.3038655          
                idNewJersey            10.201335    2.075553  4.9150 1.085e-06 ***      
                idNewMexico             2.697132    1.954022  1.3803 0.1678949          
                idNewYork              31.759614    2.946369 10.7792 < 2.2e-16 ***      
                idNorthCarolina        10.312457    2.074313  4.9715 8.192e-07 ***      
                idOhio                 13.443643    2.249611  5.9760 3.493e-09 ***      
                idOklahoma              1.082154    1.945729  0.5562 0.5782568          
                idOregon                5.281491    1.980528  2.6667 0.0078204 **       
                idPennsylvania         15.315710    2.303777  6.6481 5.619e-11 ***      
                idRhodeIsland           0.718377    1.945353  0.3693 0.7120214          
                idSouthCarolina         8.004273    2.021215  3.9601 8.184e-05 ***      
                idSouthDakota          -0.001373    1.944600 -0.0007 0.9994368          
                idTennessee             2.280171    1.950378  1.1691 0.2427279          
                idTexas                19.183765    2.372499  8.0859 2.387e-15 ***      
                idUtah                  1.981867    1.949471  1.0166 0.3096542          
                idVermont              -0.008066    1.944593 -0.0041 0.9966915          
                idVirginia              7.003185    2.004015  3.4946 0.0005019 ***      
                idWashington            9.311079    2.048825  4.5446 6.388e-06 ***      
                idWisconsin             7.131882    2.003650  3.5594 0.0003944 ***      
                time2001              -32.491734   10.397466 -3.1250 0.0018449 **       
                time2002              -30.273851    9.640997 -3.1401 0.0017532 **       
                time2003              -30.080940    8.358906 -3.5987 0.0003403 ***      
                time2004              -27.787478    5.952085 -4.6685 3.577e-06 ***      
                time2005              -24.036495    4.568201 -5.2617 1.851e-07 ***      
                time2006              -18.130395    3.681699 -4.9245 1.035e-06 ***      
                time2007              -13.487669    3.198969 -4.2163 2.779e-05 ***      
                time2008               -9.146644    3.951009 -2.3150 0.0208739 *        
                time2009               -2.599686    4.664776 -0.5573 0.5774832          
                time2010               -2.027763    4.190141 -0.4839 0.6285682          
                time2011               -3.532324    3.066164 -1.1520 0.2496643          
                time2012               -1.635736    2.804426 -0.5833 0.5598825          
                time2013               -1.569575    3.748637 -0.4187 0.6755480          
                time2014               -6.493148    4.560561 -1.4238 0.1549203          
                time2015               -0.599729    2.190506 -0.2738 0.7843227          
                time2016               -2.718167    2.003778 -1.3565 0.1753305          
                iis41                 105.954709    9.300009 11.3930 < 2.2e-16 ***      
                iis42                  83.617773    9.087714  9.2012 < 2.2e-16 ***      
                iis43                  89.692003    9.141080  9.8120 < 2.2e-16 ***      
                iis44                 118.287224    9.126764 12.9605 < 2.2e-16 ***      
                iis45                 126.493855    8.939159 14.1505 < 2.2e-16 ***      
                iis46                 201.543213    8.842194 22.7934 < 2.2e-16 ***      
                iis47                 178.333199    8.970070 19.8809 < 2.2e-16 ***      
                iis48                 208.234144    9.167989 22.7132 < 2.2e-16 ***      
                iis49                 212.088048    9.626629 22.0314 < 2.2e-16 ***      
                iis50                 161.326200   10.037956 16.0716 < 2.2e-16 ***      
                iis51                 171.448686    9.631592 17.8007 < 2.2e-16 ***      
                iis52                 163.325256    9.529325 17.1392 < 2.2e-16 ***      
                iis53                 164.576698    9.400484 17.5073 < 2.2e-16 ***      
                iis54                 112.666674    9.331818 12.0734 < 2.2e-16 ***      
                iis55                 143.291639    8.929581 16.0468 < 2.2e-16 ***      
                iis56                 145.565827    8.920149 16.3188 < 2.2e-16 ***      
                iis57                 116.837566    8.925398 13.0905 < 2.2e-16 ***      
                iis58                 134.260110    8.827127 15.2099 < 2.2e-16 ***      
                iis59                 109.369456    8.829266 12.3872 < 2.2e-16 ***      
                iis171                 27.460173    6.392377  4.2958 1.963e-05 ***      
                iis386                 28.528806    6.405204  4.4540 9.675e-06 ***      
                iis388                 47.170426    6.394515  7.3767 4.200e-13 ***      
                iis413                -20.779716    6.424790 -3.2343 0.0012714 **       
                iis593                 24.719393    6.392233  3.8671 0.0001194 ***      
                iis647                 30.230606    6.385592  4.7342 2.617e-06 ***      
                fesisNewYork.2020     -36.629488    6.407147 -5.7170 1.550e-08 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df   p-value          
                Ljung-Box AR(1)   17.301  1 3.190e-05 ***      
                Ljung-Box ARCH(1) 22.877  1 1.727e-06 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     6.14933      
                R-squared            0.97641      
                Log-lik.(n=860)  -2737.84279      

0.05

us_all

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_all (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 13:46:22 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 1020       
                Sample: 1 to 1020       
                      
                SPECIFIC mean equation:      
                      
                                               coef   std.error  t-stat   p-value          
                ar1                      5.9379e-01  2.3589e-02 25.1722 < 2.2e-16 ***      
                lgdp                     3.6680e+02  5.0179e+01  7.3098 5.915e-13 ***      
                lpop                    -3.0350e+02  3.0479e+01 -9.9579 < 2.2e-16 ***      
                lgdp_sq                 -1.2159e+01  3.0190e+00 -4.0276 6.111e-05 ***      
                avg_temp                -1.3271e+00  1.2141e+00 -1.0931 0.2746581          
                idAlaska                -1.1121e+00  1.5714e+00 -0.7077 0.4792998          
                idArizona                7.0269e+00  1.6248e+00  4.3249 1.697e-05 ***      
                idArkansas              -3.4395e-01  1.5700e+00 -0.2191 0.8266396          
                idCalifornia            -5.5266e+01  6.5792e+00 -8.4002 < 2.2e-16 ***      
                idColorado               1.0987e+01  1.6937e+00  6.4872 1.443e-10 ***      
                idConnecticut            2.0526e+01  2.2961e+00  8.9396 < 2.2e-16 ***      
                idDelaware               4.2209e+00  1.5915e+00  2.6521 0.0081401 **       
                idDistrictofColumbia     2.3446e-01  1.5698e+00  0.1494 0.8813073          
                idFlorida                1.1634e+01  1.7065e+00  6.8173 1.701e-11 ***      
                idGeorgia                3.6096e+00  1.6245e+00  2.2220 0.0265318 *        
                idHawaii                -5.9702e-02  1.5698e+00 -0.0380 0.9696712          
                idIdaho                  4.2830e-01  1.5699e+00  0.2728 0.7850599          
                idIllinois               1.1226e+01  1.7082e+00  6.5720 8.407e-11 ***      
                idIndiana                2.6684e+00  1.5771e+00  1.6920 0.0909909 .        
                idIowa                   3.6673e-01  1.5699e+00  0.2336 0.8153434          
                idKansas                -5.3924e-02  1.5698e+00 -0.0344 0.9726056          
                idKentucky               1.3054e-01  1.5698e+00  0.0832 0.9337430          
                idLouisiana              7.8750e-02  1.5698e+00  0.0502 0.9600013          
                idMaine                  2.2455e-01  1.5698e+00  0.1430 0.8862877          
                idMaryland               4.2297e+00  1.5882e+00  2.6632 0.0078789 **       
                idMassachusetts          2.1536e+01  2.1931e+00  9.8202 < 2.2e-16 ***      
                idMichigan               1.8140e+01  2.0892e+00  8.6827 < 2.2e-16 ***      
                idMinnesota              9.0026e+00  1.6588e+00  5.4273 7.361e-08 ***      
                idMississippi           -8.0664e-01  1.5707e+00 -0.5135 0.6076961          
                idMissouri               1.6847e+00  1.5725e+00  1.0714 0.2842926          
                idMontana               -6.4105e-01  1.5703e+00 -0.4082 0.6832012          
                idNebraska              -3.2526e-01  1.5700e+00 -0.2072 0.8359225          
                idNevada                 1.5815e+00  1.5726e+00  1.0057 0.3148548          
                idNewHampshire           1.9682e+00  1.5754e+00  1.2493 0.2118728          
                idNewJersey              1.0835e+01  1.9131e+00  5.6637 1.994e-08 ***      
                idNewMexico              2.6504e+00  1.5777e+00  1.6799 0.0933199 .        
                idNewYork                2.0450e+01  3.5932e+00  5.6914 1.705e-08 ***      
                idNorthCarolina          1.0137e+01  1.6786e+00  6.0387 2.273e-09 ***      
                idNorthDakota           -7.7310e-01  1.5707e+00 -0.4922 0.6226874          
                idOhio                   1.3380e+01  2.0548e+00  6.5116 1.236e-10 ***      
                idOklahoma               1.0659e+00  1.5708e+00  0.6786 0.4975522          
                idOregon                 5.1900e+00  1.6000e+00  3.2438 0.0012229 **       
                idPennsylvania           1.3573e+01  1.8844e+00  7.2027 1.249e-12 ***      
                idRhodeIsland            7.0512e-01  1.5704e+00  0.4490 0.6535436          
                idSouthCarolina          6.8203e+00  1.6531e+00  4.1258 4.039e-05 ***      
                idSouthDakota            1.2724e-04  1.5698e+00  0.0001 0.9999353          
                idTennessee              2.2436e+00  1.5747e+00  1.4248 0.1545542          
                idTexas                  1.3536e+01  2.3116e+00  5.8556 6.661e-09 ***      
                idUtah                   1.9483e+00  1.5739e+00  1.2379 0.2160825          
                idVermont               -7.2968e-03  1.5698e+00 -0.0046 0.9962923          
                idVirginia               6.8852e+00  1.6197e+00  4.2510 2.351e-05 ***      
                idWashington             8.3212e+00  2.1325e+00  3.9022 0.0001025 ***      
                idWestVirginia          -7.3220e-01  1.5705e+00 -0.4662 0.6411630          
                idWisconsin              7.0143e+00  1.6194e+00  4.3315 1.648e-05 ***      
                idWyoming               -5.6942e-01  1.5702e+00 -0.3626 0.7169589          
                time2001                -1.4720e+01  7.8804e+00 -1.8679 0.0621038 .        
                time2002                -1.3562e+01  7.3167e+00 -1.8536 0.0641224 .        
                time2003                -1.5704e+01  6.3206e+00 -2.4845 0.0131545 *        
                time2004                -1.7707e+01  4.4972e+00 -3.9372 8.880e-05 ***      
                time2005                -1.6464e+01  3.4343e+00 -4.7941 1.912e-06 ***      
                time2006                -1.1615e+01  2.7830e+00 -4.1736 3.290e-05 ***      
                time2007                -9.1374e+00  2.4221e+00 -3.7726 0.0001722 ***      
                time2008                -6.6201e+00  2.9472e+00 -2.2462 0.0249312 *        
                time2009                 8.2012e-02  3.5016e+00  0.0234 0.9813193          
                time2010                -5.2342e-01  3.1242e+00 -0.1675 0.8669848          
                time2011                -1.0183e+00  2.3033e+00 -0.4421 0.6585025          
                time2012                 2.0564e+00  2.1253e+00  0.9676 0.3335174          
                time2013                -2.0316e+00  2.7782e+00 -0.7313 0.4647992          
                time2014                -5.1548e+00  3.3751e+00 -1.5273 0.1270377          
                time2015                 1.8808e+00  1.6593e+00  1.1334 0.2573311          
                time2016                 5.2134e-01  1.5181e+00  0.3434 0.7313660          
                iis81                    1.0890e+02  7.5288e+00 14.4641 < 2.2e-16 ***      
                iis82                    8.6651e+01  7.3441e+00 11.7988 < 2.2e-16 ***      
                iis83                    9.2220e+01  7.3862e+00 12.4854 < 2.2e-16 ***      
                iis84                    1.2156e+02  7.3760e+00 16.4804 < 2.2e-16 ***      
                iis85                    1.2914e+02  7.2127e+00 17.9048 < 2.2e-16 ***      
                iis86                    2.0409e+02  7.1284e+00 28.6303 < 2.2e-16 ***      
                iis87                    1.8141e+02  7.2348e+00 25.0747 < 2.2e-16 ***      
                iis88                    2.1129e+02  7.4066e+00 28.5276 < 2.2e-16 ***      
                iis89                    2.1596e+02  7.7984e+00 27.6932 < 2.2e-16 ***      
                iis90                    1.6427e+02  8.1541e+00 20.1455 < 2.2e-16 ***      
                iis91                    1.7365e+02  7.8091e+00 22.2363 < 2.2e-16 ***      
                iis92                    1.6481e+02  7.7214e+00 21.3451 < 2.2e-16 ***      
                iis93                    1.6707e+02  7.6083e+00 21.9591 < 2.2e-16 ***      
                iis94                    1.1306e+02  7.5512e+00 14.9718 < 2.2e-16 ***      
                iis95                    1.4508e+02  7.2012e+00 20.1461 < 2.2e-16 ***      
                iis96                    1.4627e+02  7.1926e+00 20.3367 < 2.2e-16 ***      
                iis97                    1.1953e+02  7.1962e+00 16.6105 < 2.2e-16 ***      
                iis98                    1.3544e+02  7.1132e+00 19.0399 < 2.2e-16 ***      
                iis99                    1.1036e+02  7.1149e+00 15.5115 < 2.2e-16 ***      
                iis211                   2.8280e+01  5.1501e+00  5.4911 5.200e-08 ***      
                iis426                   2.7176e+01  5.1715e+00  5.2550 1.850e-07 ***      
                iis428                   4.7077e+01  5.1609e+00  9.1218 < 2.2e-16 ***      
                iis449                   2.2147e+01  5.2407e+00  4.2260 2.622e-05 ***      
                iis453                  -1.3941e+01  5.4071e+00 -2.5783 0.0100862 *        
                iis613                   2.8879e+01  5.3643e+00  5.3835 9.332e-08 ***      
                iis641                   2.0478e+01  5.8218e+00  3.5175 0.0004575 ***      
                iis642                   1.8375e+01  5.7919e+00  3.1725 0.0015626 **       
                iis644                   2.4949e+01  5.7981e+00  4.3030 1.870e-05 ***      
                iis653                   1.8765e+01  6.1496e+00  3.0514 0.0023448 **       
                iis655                   1.6508e+01  6.1699e+00  2.6755 0.0075970 **       
                iis657                   3.3404e+01  5.6160e+00  5.9479 3.887e-09 ***      
                iis707                   2.0685e+01  5.2391e+00  3.9482 8.488e-05 ***      
                iis713                   3.2191e+01  5.4263e+00  5.9324 4.259e-09 ***      
                iis717                   2.1925e+01  5.4242e+00  4.0421 5.752e-05 ***      
                iis767                   3.2742e+01  5.1536e+00  6.3531 3.349e-10 ***      
                iis770                   2.6533e+01  5.1563e+00  5.1457 3.274e-07 ***      
                iis817                   2.0996e+01  5.1481e+00  4.0783 4.938e-05 ***      
                iis869                   1.3154e+01  6.1446e+00  2.1407 0.0325664 *        
                iis951                   2.2253e+01  5.2637e+00  4.2277 2.603e-05 ***      
                fesisConnecticut.2009   -1.1333e+01  2.3000e+00 -4.9273 9.928e-07 ***      
                fesisMassachusetts.2020 -2.5343e+01  5.1642e+00 -4.9075 1.095e-06 ***      
                fesisMichigan.2013      -7.8185e+00  2.4307e+00 -3.2166 0.0013437 **       
                fesisNewJersey.2013     -5.6367e+00  2.3875e+00 -2.3609 0.0184458 *        
                fesisNewYork.2007        2.1208e+01  3.6665e+00  5.7844 1.005e-08 ***      
                fesisNewYork.2012       -2.1769e+01  4.2050e+00 -5.1770 2.784e-07 ***      
                fesisNewYork.2016       -1.0890e+01  4.3892e+00 -2.4811 0.0132786 *        
                fesisOhio.2013          -6.7539e+00  2.5509e+00 -2.6476 0.0082481 **       
                fesisTexas.2008          1.9906e+01  4.0650e+00  4.8968 1.155e-06 ***      
                fesisTexas.2011         -1.6559e+01  3.8861e+00 -4.2610 2.250e-05 ***      
                fesisWashington.2009     2.0353e+01  5.3215e+00  3.8246 0.0001400 ***      
                fesisWashington.2010    -2.2712e+01  5.2648e+00 -4.3139 1.782e-05 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df   p-value          
                Ljung-Box AR(1)   25.238  1 5.066e-07 ***      
                Ljung-Box ARCH(1) 11.475  1 0.0007056 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     4.96412      
                R-squared            0.98302      
                Log-lik.(n=1020) -3020.59860      
us_q25

                Formula: patent_count ~ lgdp + lpop + lgdp_sq + avg_temp      
                us_q25 (2000:2020); p.value: 0.05; AR: 1      
                      
                Date: Thu Mar 30 13:49:03 2023       
                Dependent var.: y       
                Method: Ordinary Least Squares (OLS)      
                Variance-Covariance: Ordinary       
                No. of observations (mean eq.): 860       
                Sample: 1 to 860       
                      
                SPECIFIC mean equation:      
                      
                                              coef   std.error   t-stat   p-value          
                ar1                     5.7187e-01  2.7433e-02  20.8458 < 2.2e-16 ***      
                lgdp                    5.1632e+02  6.1685e+01   8.3702 2.752e-16 ***      
                lpop                   -3.9780e+02  3.7637e+01 -10.5694 < 2.2e-16 ***      
                lgdp_sq                -1.9270e+01  3.7051e+00  -5.2008 2.554e-07 ***      
                avg_temp               -7.8177e-01  1.5091e+00  -0.5180 0.6045908          
                idArizona               7.4164e+00  1.8591e+00   3.9893 7.268e-05 ***      
                idCalifornia           -4.8950e+01  7.5879e+00  -6.4510 1.977e-10 ***      
                idColorado              1.1578e+01  1.9405e+00   5.9667 3.709e-09 ***      
                idConnecticut           1.4505e+01  2.0413e+00   7.1058 2.758e-12 ***      
                idDelaware              4.4645e+00  1.8198e+00   2.4533 0.0143774 *        
                idDistrictofColumbia    2.4307e-01  1.7941e+00   0.1355 0.8922666          
                idFlorida               1.2256e+01  1.9556e+00   6.2670 6.162e-10 ***      
                idGeorgia               3.9332e+00  1.8585e+00   2.1164 0.0346387 *        
                idHawaii               -6.8996e-02  1.7941e+00  -0.0385 0.9693331          
                idIdaho                 4.4764e-01  1.7942e+00   0.2495 0.8030493          
                idIllinois              1.1852e+01  1.9576e+00   6.0544 2.214e-09 ***      
                idIndiana               2.8090e+00  1.8027e+00   1.5583 0.1195878          
                idIowa                  3.8203e-01  1.7942e+00   0.2129 0.8314384          
                idKansas               -6.2680e-02  1.7941e+00  -0.0349 0.9721389          
                idKentucky              1.3669e-01  1.7941e+00   0.0762 0.9392877          
                idLouisiana             8.1426e-02  1.7941e+00   0.0454 0.9638109          
                idMaine                 2.2871e-01  1.7941e+00   0.1275 0.8985934          
                idMaryland              4.4538e+00  1.8158e+00   2.4528 0.0143997 *        
                idMassachusetts         2.1520e+01  2.4963e+00   8.6209 < 2.2e-16 ***      
                idMichigan              1.6013e+01  2.1116e+00   7.5835 9.827e-14 ***      
                idMinnesota             9.5007e+00  1.8992e+00   5.0024 7.038e-07 ***      
                idMissouri              1.7704e+00  1.7973e+00   0.9850 0.3249131          
                idNevada                1.6689e+00  1.7974e+00   0.9285 0.3534356          
                idNewHampshire          2.0921e+00  1.8007e+00   1.1618 0.2456827          
                idNewJersey             9.3298e+00  1.9473e+00   4.7912 1.994e-06 ***      
                idNewMexico             2.7972e+00  1.8034e+00   1.5510 0.1213075          
                idNewYork               3.4695e+01  2.9507e+00  11.7579 < 2.2e-16 ***      
                idNorthCarolina         1.0689e+01  1.9227e+00   5.5595 3.747e-08 ***      
                idOhio                  1.2856e+01  2.1163e+00   6.0744 1.966e-09 ***      
                idOklahoma              1.1169e+00  1.7952e+00   0.6222 0.5340243          
                idOregon                5.4775e+00  1.8298e+00   2.9936 0.0028468 **       
                idPennsylvania          1.7770e+01  2.4424e+00   7.2755 8.610e-13 ***      
                idRhodeIsland           7.4680e-01  1.7948e+00   0.4161 0.6774645          
                idSouthCarolina         8.2919e+00  1.8701e+00   4.4339 1.062e-05 ***      
                idSouthDakota          -4.5882e-03  1.7941e+00  -0.0026 0.9979601          
                idTennessee             2.3585e+00  1.7998e+00   1.3104 0.1904467          
                idTexas                 1.4160e+01  2.6566e+00   5.3304 1.293e-07 ***      
                idUtah                  2.0538e+00  1.7989e+00   1.1417 0.2539387          
                idVermont              -9.7144e-03  1.7941e+00  -0.0054 0.9956811          
                idVirginia              7.2560e+00  1.8531e+00   3.9157 9.826e-05 ***      
                idWashington            9.3354e+00  2.2815e+00   4.0918 4.738e-05 ***      
                idWisconsin             7.3839e+00  1.8527e+00   3.9855 7.384e-05 ***      
                time2001               -2.7915e+01  9.6871e+00  -2.8816 0.0040678 **       
                time2002               -2.6076e+01  8.9865e+00  -2.9017 0.0038184 **       
                time2003               -2.7145e+01  7.7786e+00  -3.4896 0.0005116 ***      
                time2004               -2.6946e+01  5.5346e+00  -4.8686 1.368e-06 ***      
                time2005               -2.4084e+01  4.2352e+00  -5.6868 1.847e-08 ***      
                time2006               -1.7976e+01  3.4204e+00  -5.2557 1.918e-07 ***      
                time2007               -1.3763e+01  2.9764e+00  -4.6239 4.424e-06 ***      
                time2008               -9.6341e+00  3.6557e+00  -2.6353 0.0085771 **       
                time2009               -2.2553e+00  4.3296e+00  -0.5209 0.6025877          
                time2010               -2.3048e+00  3.8800e+00  -0.5940 0.5526679          
                time2011               -3.1651e+00  2.8490e+00  -1.1110 0.2669391          
                time2012               -4.6830e-01  2.6118e+00  -0.1793 0.8577501          
                time2013               -2.5456e+00  3.4631e+00  -0.7351 0.4625297          
                time2014               -6.5739e+00  4.2081e+00  -1.5622 0.1186562          
                time2015                3.0172e-01  2.0375e+00   0.1481 0.8823163          
                time2016               -1.3674e+00  1.8671e+00  -0.7324 0.4641793          
                iis41                   1.0419e+02  8.6214e+00  12.0850 < 2.2e-16 ***      
                iis42                   8.2238e+01  8.4095e+00   9.7792 < 2.2e-16 ***      
                iis43                   8.8205e+01  8.4628e+00  10.4227 < 2.2e-16 ***      
                iis44                   1.1712e+02  8.4522e+00  13.8563 < 2.2e-16 ***      
                iis45                   1.2548e+02  8.2606e+00  15.1901 < 2.2e-16 ***      
                iis46                   2.0090e+02  8.1626e+00  24.6128 < 2.2e-16 ***      
                iis47                   1.7951e+02  8.2846e+00  21.6678 < 2.2e-16 ***      
                iis48                   2.0995e+02  8.4826e+00  24.7512 < 2.2e-16 ***      
                iis49                   2.1506e+02  8.9362e+00  24.0659 < 2.2e-16 ***      
                iis50                   1.6476e+02  9.3435e+00  17.6333 < 2.2e-16 ***      
                iis51                   1.7386e+02  8.9408e+00  19.4453 < 2.2e-16 ***      
                iis52                   1.6510e+02  8.8404e+00  18.6760 < 2.2e-16 ***      
                iis53                   1.6685e+02  8.7139e+00  19.1477 < 2.2e-16 ***      
                iis54                   1.1396e+02  8.6439e+00  13.1840 < 2.2e-16 ***      
                iis55                   1.4376e+02  8.2458e+00  17.4337 < 2.2e-16 ***      
                iis56                   1.4545e+02  8.2349e+00  17.6622 < 2.2e-16 ***      
                iis57                   1.1749e+02  8.2401e+00  14.2577 < 2.2e-16 ***      
                iis58                   1.3374e+02  8.1435e+00  16.4226 < 2.2e-16 ***      
                iis59                   1.0886e+02  8.1456e+00  13.3644 < 2.2e-16 ***      
                iis171                  2.7747e+01  5.8997e+00   4.7031 3.043e-06 ***      
                iis386                  2.8202e+01  5.9110e+00   4.7710 2.198e-06 ***      
                iis388                  4.7604e+01  5.9002e+00   8.0682 2.780e-15 ***      
                iis409                  2.3642e+01  5.9005e+00   4.0068 6.761e-05 ***      
                iis413                 -1.8538e+01  5.9411e+00  -3.1203 0.0018748 **       
                iis513                  2.5003e+01  5.8954e+00   4.2412 2.498e-05 ***      
                iis544                  1.2049e+01  5.9567e+00   2.0227 0.0434512 *        
                iis557                  3.1515e+01  6.4283e+00   4.9025 1.158e-06 ***      
                iis587                  2.1326e+01  5.9015e+00   3.6137 0.0003218 ***      
                iis593                  2.6350e+01  5.9076e+00   4.4603 9.421e-06 ***      
                iis647                  2.8725e+01  5.9995e+00   4.7879 2.026e-06 ***      
                iis650                  2.2657e+01  5.9993e+00   3.7766 0.0001714 ***      
                fesisNewYork.2016      -2.3261e+01  3.2716e+00  -7.1101 2.678e-12 ***      
                fesisPennsylvania.2014 -8.2538e+00  2.7806e+00  -2.9684 0.0030880 **       
                fesisTexas.2008         2.3867e+01  4.0086e+00   5.9538 4.001e-09 ***      
                fesisTexas.2011        -1.9562e+01  3.7824e+00  -5.1717 2.969e-07 ***      
                fesisWashington.2011    1.8971e+01  6.0252e+00   3.1486 0.0017046 **       
                fesisWashington.2012   -2.0385e+01  6.0578e+00  -3.3651 0.0008036 ***      
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                      
                Diagnostics and fit:      
                      
                                  Chi-sq df p-value         
                Ljung-Box AR(1)   9.9142  1 0.00164 **      
                Ljung-Box ARCH(1) 5.4737  1 0.01930 *       
                ---      
                Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1      
                                                  
                SE of regression     5.67329      
                R-squared            0.98021      
                Log-lik.(n=860)  -2663.04833